Knowledge base / release channel
The reviewed release.
Evidence before labels.
A governed library of production-minded FinTech topics. Visible articles have cleared the current release manifest; draft and review-blocked packages remain outside this index until repaired.
747 released articles in this view
Financial Mathematics, Statistics, and Data Foundations / Mathematical Language and Quantitative Reasoning
Variables, Constants, Expressions, and Equations
Learn to read a financial formula as a small sentence about money.Financial Mathematics, Statistics, and Data Foundations / Mathematical Language and Quantitative Reasoning
Functions, Domains, Ranges, and Graphs
See a function as a rule that turns an allowed input into one output.Financial Mathematics, Statistics, and Data Foundations / Mathematical Language and Quantitative Reasoning
Ratios, Proportions, Rates, and Percentages
Compare amounts fairly by making the denominator and the unit visible.Financial Mathematics, Statistics, and Data Foundations / Mathematical Language and Quantitative Reasoning
Percentage Change, Percentage Points, and Basis Points
Use three different languages for change without mixing them up.Financial Mathematics, Statistics, and Data Foundations / Mathematical Language and Quantitative Reasoning
Exponents, Roots, and Logarithms
Understand growth, undoing a power, and asking “which power?” in plain language.Financial Mathematics, Statistics, and Data Foundations / Mathematical Language and Quantitative Reasoning
Summation, Products, and Index Notation
Read a compact list instruction as “add these” or “multiply these.”Financial Mathematics, Statistics, and Data Foundations / Mathematical Language and Quantitative Reasoning
Linear Equations and Systems
Find unknown amounts when several simple balances must be true at once.Financial Mathematics, Statistics, and Data Foundations / Mathematical Language and Quantitative Reasoning
Inequalities, Bounds, and Constraints
Describe what is allowed when the answer is a safe range, not one exact number.Financial Mathematics, Statistics, and Data Foundations / Mathematical Language and Quantitative Reasoning
Units, Dimensions, Scale, and Normalization
Keep the meaning attached to every number, even when the scale changes.Financial Mathematics, Statistics, and Data Foundations / Mathematical Language and Quantitative Reasoning
Rounding, Precision, Tolerance, and Significant Digits
Show only as many digits as the information can honestly support.Financial Mathematics, Statistics, and Data Foundations / Financial Arithmetic, Time Value, and Returns
Simple Interest
See how a fixed rate adds interest to the original amount without adding yesterday's interest to today's base.Financial Mathematics, Statistics, and Data Foundations / Financial Arithmetic, Time Value, and Returns
Compound Interest
See how each period can earn interest on the amount already built up, not only on the starting amount.Financial Mathematics, Statistics, and Data Foundations / Financial Arithmetic, Time Value, and Returns
Present Value and Future Value
Translate money at one date into an equivalent amount at another date using a stated growth rate.Financial Mathematics, Statistics, and Data Foundations / Financial Arithmetic, Time Value, and Returns
Discount Factors and Discount Rates
Use one small factor to show how much of a future amount is worth at an earlier date.Financial Mathematics, Statistics, and Data Foundations / Financial Arithmetic, Time Value, and Returns
Cash-Flow Timelines and Net Present Value
Place each cash flow on a timeline, translate each one to the same date, and add the signed values.Financial Mathematics, Statistics, and Data Foundations / Financial Arithmetic, Time Value, and Returns
Simple Return
Measure the change from a starting investment to an ending value, including cash received along the way.Financial Mathematics, Statistics, and Data Foundations / Financial Arithmetic, Time Value, and Returns
Log Return
Use the natural logarithm of the ending value divided by the starting value to describe multiplicative change on an additive scale.Financial Mathematics, Statistics, and Data Foundations / Financial Arithmetic, Time Value, and Returns
Holding-Period and Cumulative Return
Combine several period returns by multiplying their growth factors, then compare the result with the start of the whole path.Financial Mathematics, Statistics, and Data Foundations / Financial Arithmetic, Time Value, and Returns
Arithmetic versus Geometric Average Return
Use a simple average to describe a typical one-period rate, and a geometric average to summarize a compounded path.Financial Mathematics, Statistics, and Data Foundations / Financial Arithmetic, Time Value, and Returns
Return Annualization and Deannualization
Translate a return over one length of time into an equivalent yearly rate, or reverse that translation, using compounding.Financial Mathematics, Statistics, and Data Foundations / Data, Variables, Samples, and Measurement
Observations, Entities, Variables, and Datasets
An entity is the thing we study, an observation is one recorded case, a variable is a named property, and a dataset is an organized collection of observations.Financial Mathematics, Statistics, and Data Foundations / Data, Variables, Samples, and Measurement
Numeric, Categorical, Ordinal, and Binary Variables
Numeric values support arithmetic, categorical values name groups, ordinal values have an order but not a trustworthy distance, and binary values represent two states.Financial Mathematics, Statistics, and Data Foundations / Data, Variables, Samples, and Measurement
Population, Sample, Census, and Sampling Frame
The population is the full group of interest, a sample is the observed subset, a census attempts to measure every population member, and a sampling frame is the operational list from which selection occurs.Financial Mathematics, Statistics, and Data Foundations / Data, Variables, Samples, and Measurement
Cross-Sectional, Time-Series, Panel, and Event Data
Cross-sectional data varies mainly across entities, time-series data follows one unit across time, panel data follows multiple entities across time, and event data records occurrences at event times.Financial Mathematics, Statistics, and Data Foundations / Data, Variables, Samples, and Measurement
Identifiers, Keys, Joins, and Data Grain
An identifier names an entity, a key uniquely identifies a record at the declared grain, and a join combines records according to matching keys.Financial Mathematics, Statistics, and Data Foundations / Data, Variables, Samples, and Measurement
Timestamps, Time Zones, Calendars, and Observation Time
A timestamp needs an instant or timezone context, while a calendar defines valid business dates; observation time should remain distinct from ingestion and publication time.Financial Mathematics, Statistics, and Data Foundations / Data, Variables, Samples, and Measurement
Missing, Nonfinite, Censored, and Truncated Values
Missing means no usable value is present, nonfinite includes infinities and NaN-like numerical states, censoring preserves a bound without the exact value, and truncation removes cases outside a selection boundary.Financial Mathematics, Statistics, and Data Foundations / Data, Variables, Samples, and Measurement
Measurement Error, Resolution, Accuracy, and Precision
Error is measured minus reference, accuracy concerns closeness to an accepted reference, precision concerns repeatability, and resolution is the smallest display or recording increment.Financial Mathematics, Statistics, and Data Foundations / Data, Variables, Samples, and Measurement
Revisions, Vintages, and Point-in-Time Availability
A revision changes a previously reported value, a vintage is the dataset as known at a particular time, and point-in-time retrieval selects only records available by the as-of cutoff.Financial Mathematics, Statistics, and Data Foundations / Data, Variables, Samples, and Measurement
Data Provenance, Lineage, Ownership, and Licensing
Provenance records origin, lineage records transformations, ownership assigns stewardship, and licensing states permitted use.Financial Mathematics, Statistics, and Data Foundations / Location, Ranking, and Exploratory Summaries
Count, Sum, Minimum, Maximum, and Range
Reduces one numeric series to the five headline aggregates: how many observations there are, their total, the smallest and largest value, and the distance between those extremes.Financial Mathematics, Statistics, and Data Foundations / Location, Ranking, and Exploratory Summaries
Arithmetic Mean
Divides the sum of a numeric series by the number of observations and reports both the mean and the count it was divided by.Financial Mathematics, Statistics, and Data Foundations / Location, Ranking, and Exploratory Summaries
Weighted Mean
Computes a weighted average of values using the parallel weights series, dividing the sum of value-times-weight products by the total weight.Financial Mathematics, Statistics, and Data Foundations / Location, Ranking, and Exploratory Summaries
Median and Mode
Reports the middle of a numeric series and its most frequent values, tallying exact equality so a tie produces several modes rather than one arbitrary winner.Financial Mathematics, Statistics, and Data Foundations / Location, Ranking, and Exploratory Summaries
Trimmed and Winsorized Means
Cuts the same number of observations off each tail of the sorted series and averages what is left, then averages again with those tails replaced by the surviving boundary values instead of discarded.Financial Mathematics, Statistics, and Data Foundations / Location, Ranking, and Exploratory Summaries
Percentiles, Quantiles, and Quartiles
Returns the three quartiles of a numeric series and the interquartile range between the first and third, using linear interpolation between neighbouring order statistics.Financial Mathematics, Statistics, and Data Foundations / Location, Ranking, and Exploratory Summaries
Ranks, Ties, and Percentile Rank
Assigns each observation its position in the sorted series, giving tied observations the average of the positions they span, and rescales those ranks onto a 0-to-100 percentile scale.Financial Mathematics, Statistics, and Data Foundations / Location, Ranking, and Exploratory Summaries
Frequency Tables and Relative Frequency
Counts how often each distinct value occurs in a numeric series and expresses those counts as shares of the total.Financial Mathematics, Statistics, and Data Foundations / Location, Ranking, and Exploratory Summaries
Histograms and Empirical Distribution Functions
Splits the observed span into equal-width bins and counts the observations in each, alongside the empirical distribution function evaluated at every sorted observation.Financial Mathematics, Statistics, and Data Foundations / Location, Ranking, and Exploratory Summaries
Five-Number Summary and Box Plot
Produces the minimum, three quartiles, and maximum of a numeric series, the Tukey 1.5-IQR fences drawn from them, and the observations lying outside those fences.Financial Mathematics, Statistics, and Data Foundations / Dispersion, Shape, and Robust Statistics
Deviation, Absolute Deviation, and Squared Deviation
Centres a numeric series on its arithmetic mean and returns the three per-observation distance forms built from that centring: signed, absolute, and squared.Financial Mathematics, Statistics, and Data Foundations / Dispersion, Shape, and Robust Statistics
Range and Interquartile Range
Measures spread two ways on the same series: the full distance from smallest to largest, and the distance covering the middle half between the first and third quartiles.Financial Mathematics, Statistics, and Data Foundations / Dispersion, Shape, and Robust Statistics
Mean Absolute Deviation
Averages the absolute distances of the observations from their arithmetic mean, giving a spread figure in the same units as the data and without squaring.Financial Mathematics, Statistics, and Data Foundations / Dispersion, Shape, and Robust Statistics
Median Absolute Deviation
Takes the median of the absolute distances from the series median, and rescales it by 1.4826 so it lines up with a standard deviation under normality.Financial Mathematics, Statistics, and Data Foundations / Dispersion, Shape, and Robust Statistics
Population and Sample Variance
Averages the squared deviations from the mean twice over the same series: once dividing by the observation count, once by that count less one.Financial Mathematics, Statistics, and Data Foundations / Dispersion, Shape, and Robust Statistics
Population and Sample Standard Deviation
Takes the square root of both the population and the sample variance of one series, returning spread in the same units as the observations.Financial Mathematics, Statistics, and Data Foundations / Dispersion, Shape, and Robust Statistics
Coefficient of Variation and Scale Comparability
Divides the sample standard deviation by the absolute value of the mean, turning spread into a unit-free figure that can be compared across series measured on different scales.Financial Mathematics, Statistics, and Data Foundations / Dispersion, Shape, and Robust Statistics
Z-Score, Robust Z-Score, and Standardization
Standardises every observation twice: once against the mean and sample standard deviation, and once against the median and median absolute deviation scaled by 0.67448975.Financial Mathematics, Statistics, and Data Foundations / Dispersion, Shape, and Robust Statistics
Skewness and Tail Asymmetry
Divides the third central moment by the second raised to the power 1.5, giving the moment coefficient of skewness, and labels which tail is the longer one.Financial Mathematics, Statistics, and Data Foundations / Dispersion, Shape, and Robust Statistics
Kurtosis, Excess Kurtosis, and Tail Weight
Divides the fourth central moment by the square of the second, subtracts 3 to give excess kurtosis, and says whether the tails are heavier or lighter than a normal distribution's.Financial Mathematics, Statistics, and Data Foundations / Probability and Random Variables
Experiments, Outcomes, Sample Spaces, and Events
Sizes a sample space and a candidate event, and checks that every outcome named in the event actually appears in the sample space.Financial Mathematics, Statistics, and Data Foundations / Probability and Random Variables
Probability Rules, Complements, Unions, and Intersections
Applies the complement and addition rules to a pair of events, deriving the probability that A does not happen and the probability that at least one of A or B happens.Financial Mathematics, Statistics, and Data Foundations / Probability and Random Variables
Conditional Probability
Rescales the joint probability of two events by each marginal in turn, giving the probability of A once B is known and the probability of B once A is known.Financial Mathematics, Statistics, and Data Foundations / Probability and Random Variables
Independence and Dependence
Compares the observed joint probability of two events against the product of their marginals, and reports both the verdict and the size of the gap.Financial Mathematics, Statistics, and Data Foundations / Probability and Random Variables
Bayes' Theorem and Base Rates
Turns a prior, a true-positive rate, and a false-positive rate into the posterior probability of the condition given a positive result, along with the unconditional probability of that result.Financial Mathematics, Statistics, and Data Foundations / Probability and Random Variables
Discrete and Continuous Random Variables
Validates a discrete random variable given as a support and a matching probability vector, echoing back the declared kind, the support, and the total mass it carries.Financial Mathematics, Statistics, and Data Foundations / Probability and Random Variables
Expected Value
Weights each value of a discrete random variable by its probability and sums the result, keeping the individual products so the total can be read term by term.Financial Mathematics, Statistics, and Data Foundations / Probability and Random Variables
Variance, Moments, and Moment-Generating Intuition
Computes the first two raw moments of a discrete random variable and derives its variance as the second raw moment less the square of the first.Financial Mathematics, Statistics, and Data Foundations / Probability and Random Variables
Joint, Marginal, and Conditional Distributions
Collapses a joint probability table over each axis in turn to give the two marginal distributions, then renormalises one slice of it to give the conditional distribution of X at a chosen value of Y.Financial Mathematics, Statistics, and Data Foundations / Probability and Random Variables
Covariance and Correlation of Random Variables
Computes the probability-weighted covariance of the two variables in a joint distribution table and divides it by the product of their standard deviations to give the correlation.Financial Mathematics, Statistics, and Data Foundations / Probability Distributions and Simulation Basics
PMF, PDF, CDF, Survival, and Quantile Functions
Reads an empirical sample from input.values and reports where the threshold input.x sits inside it, plus the sample quantile at probability input.p.Financial Mathematics, Statistics, and Data Foundations / Probability Distributions and Simulation Basics
Bernoulli and Binomial Distributions
Computes the Bernoulli mean and the binomial probability mass and cumulative probability for k successes in n independent trials with success probability p.Financial Mathematics, Statistics, and Data Foundations / Probability Distributions and Simulation Basics
Poisson Distribution and Event Counts
Evaluates the Poisson probability of exactly k events, the cumulative probability of at most k, and the distribution's mean and variance, for a rate of lambda events per interval.Financial Mathematics, Statistics, and Data Foundations / Probability Distributions and Simulation Basics
Uniform Distribution and Random Sampling
Draws sampleCount values on the unit interval from a seeded linear congruential generator and reports the draws with their support and realised mean.Financial Mathematics, Statistics, and Data Foundations / Probability Distributions and Simulation Basics
Normal Distribution and Standard Normal
Evaluates the normal density and cumulative probability at input.x for a distribution with mean mu and standard deviation sigma, and returns the standardised score that maps x onto the standard normal.Financial Mathematics, Statistics, and Data Foundations / Probability Distributions and Simulation Basics
Lognormal Distribution and Positive Quantities
Evaluates the lognormal density and cumulative probability at input.x for a variable whose logarithm is normal with mean mu and standard deviation sigma, and returns the distribution's median.Financial Mathematics, Statistics, and Data Foundations / Probability Distributions and Simulation Basics
Student-t Distribution and Heavy Tails
Evaluates the Student t density at input.x for df degrees of freedom and reports the distribution's variance, which only exists once df passes two.Financial Mathematics, Statistics, and Data Foundations / Probability Distributions and Simulation Basics
Exponential, Gamma, and Weibull Waiting-Time Models
Evaluates three waiting-time models at the same point input.x: the exponential survival function, the gamma density, and the Weibull survival function, all sharing shape and scale.Financial Mathematics, Statistics, and Data Foundations / Probability Distributions and Simulation Basics
Mixture Distributions, Multimodality, and Fat Tails
Evaluates a weighted mixture of normal components at input.x, which is how a single series can show more than one mode and fatter tails than any of its parts.Financial Mathematics, Statistics, and Data Foundations / Probability Distributions and Simulation Basics
Random Sampling and Monte Carlo Intuition
Estimates the probability p by counting how many of sampleCount seeded uniform draws land at or below it, and reports how far that Monte Carlo estimate lands from the known answer.Financial Mathematics, Statistics, and Data Foundations / Sampling, Estimation, and Statistical Inference
Parameters, Statistics, Estimands, and Estimators
Places the known population parameter from input.populationMean alongside the statistic computed from input.sample, and names which side is the estimand and which is the estimator.Financial Mathematics, Statistics, and Data Foundations / Sampling, Estimation, and Statistical Inference
Sampling Distributions
Summarises the replicated estimates in input.estimates as a sampling distribution: where it centres, how wide it is, and how many replications produced it.Financial Mathematics, Statistics, and Data Foundations / Sampling, Estimation, and Statistical Inference
Estimator Bias, Consistency, Efficiency, and Robustness
Scores an estimator against a known truth: the average error of the replicated estimates, their mean squared error, a robust median estimate, and whether the mean squared error clears mseBenchmark.Financial Mathematics, Statistics, and Data Foundations / Sampling, Estimation, and Statistical Inference
Law of Large Numbers
Walks the running mean of input.sample one observation at a time and reports how far it has drifted from input.populationMean by the end.Financial Mathematics, Statistics, and Data Foundations / Sampling, Estimation, and Statistical Inference
Central Limit Theorem
Standardises the replicated estimates in input.estimates by subtracting populationMean and dividing by their spread, then checks how close the standardised values sit to zero.Financial Mathematics, Statistics, and Data Foundations / Sampling, Estimation, and Statistical Inference
Standard Error
Reports the standard error of the mean for input.sample — its sample standard deviation divided by the square root of the observation count.Financial Mathematics, Statistics, and Data Foundations / Sampling, Estimation, and Statistical Inference
Confidence Intervals and Coverage
Builds a two-sided interval around the mean of input.sample and reports whether populationMean falls inside it.Financial Mathematics, Statistics, and Data Foundations / Sampling, Estimation, and Statistical Inference
Null and Alternative Hypotheses
States a two-sided test of the mean of input.sample against input.nullMean, and returns the z statistic with the reject-or-not decision taken at the fixed critical value 1.959963984540054.Financial Mathematics, Statistics, and Data Foundations / Sampling, Estimation, and Statistical Inference
P-Values, Significance, Type I/II Errors, and Power
Turns the two-sided z statistic for input.sample against input.nullMean into a p-value, compares it with alpha, and approximates the test's power at input.alternativeMean.Financial Mathematics, Statistics, and Data Foundations / Sampling, Estimation, and Statistical Inference
Effect Size, Practical Significance, and Multiple Comparisons
Reports a standardised effect size for the gap between the mean of input.sample and input.nullMean, tests that gap against a practical threshold, and splits alpha across input.comparisons tests Bonferroni-style.Financial Mathematics, Statistics, and Data Foundations / Dependence, Regression, and Model Foundations
Scatter Plots, Association, and Nonlinear Patterns
Pairs input.x and input.y into plottable points and reports the Pearson correlation over them along with its sign.Financial Mathematics, Statistics, and Data Foundations / Dependence, Regression, and Model Foundations
Sample Covariance Calculation and Interpretation
Computes the sample covariance between input.x and input.y using the n-1 denominator, and reports which way the two series move together.Financial Mathematics, Statistics, and Data Foundations / Dependence, Regression, and Model Foundations
Pearson Correlation Calculation and Interpretation
Computes the Pearson correlation between input.x and input.y and its absolute value as a sign-free strength score.Financial Mathematics, Statistics, and Data Foundations / Dependence, Regression, and Model Foundations
Spearman Rank Correlation and Kendall Tau
Replaces input.x and input.y with their ranks, averaging ranks across ties, then reports the Spearman correlation of those ranks and Kendall's tau-a from the concordant and discordant pair counts.Financial Mathematics, Statistics, and Data Foundations / Dependence, Regression, and Model Foundations
Correlation, Causation, Confounding, and Spurious Relationships
Contrasts the pooled correlation of input.x and input.y with the correlation recomputed inside each label in input.groups, which is where a confounded or reversed relationship shows itself.Financial Mathematics, Statistics, and Data Foundations / Dependence, Regression, and Model Foundations
Simple Ordinary Least Squares Regression
Fits a single-predictor ordinary least squares line of input.y on input.x and returns the fitted coefficients with the in-sample fitted values.Financial Mathematics, Statistics, and Data Foundations / Dependence, Regression, and Model Foundations
Intercepts, Slopes, Coefficients, and Predictions
Fits the least squares line of input.y on input.x and evaluates it at one new predictor value, input.predictX.Financial Mathematics, Statistics, and Data Foundations / Dependence, Regression, and Model Foundations
Residuals, MAE, MSE, and RMSE
Returns the least squares residuals of input.y on input.x together with the three usual summaries of their size.Financial Mathematics, Statistics, and Data Foundations / Dependence, Regression, and Model Foundations
R-Squared and Adjusted R-Squared
Reports the share of the variation in input.y that the least squares fit on input.x accounts for, and the same figure adjusted for the one estimated slope.Financial Mathematics, Statistics, and Data Foundations / Dependence, Regression, and Model Foundations
Regression Assumptions, Heteroskedasticity, and Multicollinearity
Runs three diagnostics on the least squares fit of y on x: the mean residual, a stand-in for non-constant error variance, and a stand-in for collinearity with a second predictor.Financial Mathematics, Statistics, and Data Foundations / Financial Time-Series Foundations
Time Order, Frequency, Regularity, and Financial Calendars
Checks whether a timestamped series runs in chronological order and whether its observations are evenly spaced, reporting the common spacing in seconds when there is one.Financial Mathematics, Statistics, and Data Foundations / Financial Time-Series Foundations
Levels, Changes, Differences, and Returns
Converts a level series into its period-over-period differences and its simple returns, keeping the original levels alongside them.Financial Mathematics, Statistics, and Data Foundations / Financial Time-Series Foundations
Lags, Leads, and Temporal Dependence
Pairs every observation with the value lag positions behind it, and exposes the same series shifted forward as the lead.Financial Mathematics, Statistics, and Data Foundations / Financial Time-Series Foundations
Rolling and Expanding Windows
Computes a fixed-length rolling mean of the series next to its expanding mean, so a window that forgets can be compared with one that never does.Financial Mathematics, Statistics, and Data Foundations / Financial Time-Series Foundations
Resampling, Aggregation, and Time Alignment
Cuts the series into consecutive fixed-size buckets and averages each one, coarsening the sampling frequency.Financial Mathematics, Statistics, and Data Foundations / Financial Time-Series Foundations
Trend, Seasonality, Cycles, and Remainder
Separates a series into a rolling-mean trend, a seasonal difference taken period steps back, and the remainder left once the trend is removed.Financial Mathematics, Statistics, and Data Foundations / Financial Time-Series Foundations
Autocovariance and Autocorrelation
Measures how far a series moves with its own past at a given lag, using the population convention that divides by the full observation count.Financial Mathematics, Statistics, and Data Foundations / Financial Time-Series Foundations
Stationarity and Differencing Intuition
Compares the average level of the second half of a series with the first half, and reports the first differences, as a rough read on whether the level drifts.Financial Mathematics, Statistics, and Data Foundations / Financial Time-Series Foundations
Smoothing, Baselines, and Naive Forecasts
Runs simple exponential smoothing over the series and reports both the naive last-value forecast and the smoothed one.Financial Mathematics, Statistics, and Data Foundations / Financial Time-Series Foundations
Look-Ahead Leakage and Time-Aware Data Splits
Splits a timestamped series at a given position and reports whether the training block reaches into the testing block's time range.Financial Mathematics, Statistics, and Data Foundations / Financial Risk and Performance Statistics
Volatility and Annualized Volatility
Takes the sample standard deviation of a return series and rescales it to an annual horizon by the square root of the observations per year.Financial Mathematics, Statistics, and Data Foundations / Financial Risk and Performance Statistics
Downside Deviation and Target Shortfall
Measures dispersion of returns below a target only, so upside swings do not count as risk.Financial Mathematics, Statistics, and Data Foundations / Financial Risk and Performance Statistics
Drawdown and Maximum Drawdown
Compounds a return series into a wealth path and tracks how far that path sits below its own running peak.Financial Mathematics, Statistics, and Data Foundations / Financial Risk and Performance Statistics
Loss Distributions and Loss Quantiles
Flips a return series into losses, sorts them, and reads off the quantile at the requested confidence by linear interpolation between neighbours.Financial Mathematics, Statistics, and Data Foundations / Financial Risk and Performance Statistics
Value at Risk Intuition
Reads historical value at risk straight off the sorted loss series and counts how many observed losses ran past it.Financial Mathematics, Statistics, and Data Foundations / Financial Risk and Performance Statistics
Expected Shortfall Intuition
Averages the losses that sit at or beyond the value-at-risk threshold, describing the tail rather than only its edge.Financial Mathematics, Statistics, and Data Foundations / Financial Risk and Performance Statistics
Beta and Market-Relative Risk
Divides the sample covariance between a return series and its benchmark by the benchmark's sample variance.Financial Mathematics, Statistics, and Data Foundations / Financial Risk and Performance Statistics
Sharpe, Sortino, and Information Ratio Intuition
Computes three reward-per-unit-of-risk ratios from the same series, each dividing an average by a different notion of risk.Financial Mathematics, Statistics, and Data Foundations / Financial Risk and Performance Statistics
Active Return and Tracking Error
Subtracts the benchmark from the portfolio period by period, then reports the average and the annualized volatility of that difference.Financial Mathematics, Statistics, and Data Foundations / Financial Risk and Performance Statistics
Covariance Matrices, Portfolio Variance, and Diversification
Combines portfolio weights with a covariance matrix into portfolio variance, and isolates the share of it that comes from the off-diagonal terms.Financial Mathematics, Statistics, and Data Foundations / Statistical Computing and Reproducibility
Floating-Point Representation, Overflow, and Underflow
Inspects one double-precision number: whether it is finite, how large one representable step at its magnitude is, and whether squaring it would stay inside a stated magnitude ceiling.Financial Mathematics, Statistics, and Data Foundations / Statistical Computing and Reproducibility
Stable Summation and Mean Calculation
Adds a list twice, once straight left to right and once carrying a running compensation term, so the two totals can be put side by side.Financial Mathematics, Statistics, and Data Foundations / Statistical Computing and Reproducibility
Stable Online Variance and Welford's Algorithm
Runs Welford's single-pass update to produce the mean and sample variance without ever accumulating a sum of raw squares.Financial Mathematics, Statistics, and Data Foundations / Statistical Computing and Reproducibility
Batch, Rolling, and Streaming Statistic Equivalence
Computes the same fixed-window mean two ways, by re-averaging each window slice and by a running add-and-drop sum, then checks that they agree.Financial Mathematics, Statistics, and Data Foundations / Statistical Computing and Reproducibility
Missing, Infinite, Invalid, and Unsupported-State Policies
Screens a mixed raw list down to the entries that are genuinely finite numbers and reports how many were turned away.Financial Mathematics, Statistics, and Data Foundations / Statistical Computing and Reproducibility
Pseudorandom Numbers, Seeds, and Reproducibility
Draws a run of unit-interval numbers from a seeded linear congruential generator, so the same seed always replays the same stream.Financial Mathematics, Statistics, and Data Foundations / Statistical Computing and Reproducibility
Vectorization, Index Alignment, and Shape Safety
Inner-joins two labelled vectors on their index field and reports what each side lost in the process.Financial Mathematics, Statistics, and Data Foundations / Statistical Computing and Reproducibility
Leakage-Free Fitting, Scaling, and Preprocessing
Fits a standardizing centre and scale on the training split alone, then applies that one transform to both splits.Financial Mathematics, Statistics, and Data Foundations / Statistical Computing and Reproducibility
Fixtures, Numerical Tolerances, and Property Tests
Compares an actual vector against an expected one under an absolute tolerance, the way a fixture check does.Financial Mathematics, Statistics, and Data Foundations / Statistical Computing and Reproducibility
Reproducible Analysis, Metadata, and Audit Trails
Serializes a run's inputs, method, version and seed into a deterministic JSON string and fingerprints it with a 32-bit FNV-1a hash.Market Data Engineering / Bar Construction
Time Bars
Groups a trade tape into fixed-duration bars. This is the sampling scheme every chart you have seen uses, and it is a *choice*: it samples the market at a constant rate regardless of how much is happening in it.Market Data Engineering / Bar Construction
Tick Bars
Closes a bar every N trades rather than every N seconds. Bars then arrive at the rate the market is transacting, so quiet periods produce fewer of them.Market Data Engineering / Bar Construction
Volume Bars
Closes a bar once a target share volume has traded. Sampling by volume rather than by clock gives series with far more stable statistical properties than time bars.Market Data Engineering / Bar Construction
Dollar Bars
Closes a bar once a target traded *value* is reached. Unlike volume bars this stays comparable as the price level changes — 1,000 shares of a $10 stock and of a $500 stock are not the same event.Market Data Engineering / Bar Construction
Tick-Imbalance Bars
Closes a bar when signed tick flow becomes unusually one-sided relative to what recent history led you to expect.Market Data Engineering / Bar Construction
Volume-Imbalance Bars
The imbalance rule applied to signed *volume* rather than signed tick count, so one large order weighs more than many small ones pointing the same way.Market Data Engineering / Bar Construction
Tick-Run Bars
Closes a bar when a run of same-signed trades exceeds what the recent buy probability makes plausible.Market Data Engineering / Cleaning and Validation
OHLC Consistency Validator
Checks each bar against the invariants an OHLC bar must satisfy — high is the maximum, low is the minimum, open and close lie between them — with a tick-size tolerance so representable rounding is not reported as corruption.Market Data Engineering / Cleaning and Validation
Hampel Bad-Tick Filter
Flags points that sit too far from a rolling median, measured in robust deviations rather than standard deviations — so one fat-finger print cannot inflate the very statistic used to detect it.Market Data Engineering / Cleaning and Validation
Median Absolute Deviation Outlier Filter
Whole-sample outlier detection against the median absolute deviation.Market Data Engineering / Cleaning and Validation
Stale-Quote Detector
Separates the several distinct ways a quote can be stale: old at the source, delayed in transport, unchanged for too long, or arriving after a missed heartbeat.Market Data Engineering / Cleaning and Validation
Duplicate-Trade Resolver
Reconciles a stream of new, corrected and cancelled trade messages into one authoritative set.Market Data Engineering / Cleaning and Validation
Crossed/Locked Market Detector
Classifies a quote as normal, locked (bid equals ask) or crossed (bid above ask).Market Data Engineering / Time Synchronization
Previous-Tick Interpolation
Samples a series onto a grid by carrying the last value known *at that moment* forward.Market Data Engineering / Time Synchronization
Linear Quote Interpolation
Interpolates between the quotes either side of a target time. Not causal, and no accuracy advantage over carrying the previous quote forward is claimed.Market Data Engineering / Time Synchronization
Refresh-Time Sampling
Builds a common clock for several instruments by advancing only when every one of them has refreshed. One established construction, not the standard remedy.Market Data Engineering / Time Synchronization
Exchange-Calendar Alignment
Validates a trading-calendar bundle before anything is aligned to it: that sessions do not overlap, that closures are consistent with sessions, and that the licence terms permitting redistribution are present.Market Data Engineering / Time Synchronization
Asynchronous Return Alignment
Compares two return intervals and reports exactly how they overlap.Market Data Engineering / Data Quality
Missing-Bar Gap Classifier
Decides why a bar is missing: the session was closed, the instrument was halted, the feed dropped, or a sequence number was skipped.Market Data Engineering / Data Quality
Feed-Latency Monitor
Validates that a latency measurement is meaningful before any latency is computed from it.Market Data Engineering / Data Quality
Price-Source Consensus Check
Reconciles quotes from several providers into one defensible price, or refuses to.Market Data Engineering / Data Quality
Schema-Drift Detector: Catch Structural and Semantic Contract Changes
Compares two versions of a feed schema and classifies every change as compatible or breaking.Market Data Engineering / Data Quality
Point-in-Time Availability Guard
Reconstructs what was actually knowable at a given moment, using each record's available_at rather than its observation_time.Market Data Engineering / Data Quality
Provider Adjustment-Basis Drift Detector
Compares archived provider adjustment factors and isolates unexplained residual drift after newly knowable corporate actions.Market Data Engineering / Order-Book Feed Engineering
Trade-and-Quote Event Normalization
Normalises raw venue trade and quote messages into one canonical event shape.Market Data Engineering / Order-Book Feed Engineering
Level-2 Snapshot-and-Delta Reconstruction
Rebuilds an aggregated price-level book from a snapshot plus the deltas that follow it.Market Data Engineering / Order-Book Feed Engineering
Level-3 Order-by-Order Reconstruction
Rebuilds the book order by order rather than by price level. Each visible order keeps its identity and quantity; the emitted priority_rank is insertion order within the reconstructed stream, not a venue queue position.Market Data Engineering / Order-Book Feed Engineering
Sequence-Gap Detection and Recovery
Detects missing sequence numbers and decides whether the stream can continue or must resynchronise from a snapshot.Market Data Engineering / Order-Book Feed Engineering
Price-Level Quantity Aggregation
Collapses individual orders into quantity per price level — the Level 3 to Level 2 projection, and the form most analytics actually consume.Market Data Engineering / Order-Book Feed Engineering
Snapshot/Incremental-Feed Reconciliation
Reconciles a periodic snapshot against the book built from incrementals.Market Data Engineering / Order-Book Feed Engineering
Multi-Venue Best-Quote and Book Consolidation
Merges books from several venues into one consolidated view and identifies the best bid and offer across them.Corporate Actions and Security Master Data / Adjustment Factors
Backward Split Adjustment
Restates prices before a split onto the post-split basis so the series is continuous across the event.Corporate Actions and Security Master Data / Adjustment Factors
Forward Split Adjustment: carry later observations onto an earlier share basis
Restates a series onto a chosen basis date rather than onto the latest one, so a figure quoted in a historical report can still be reproduced after subsequent splits.Corporate Actions and Security Master Data / Adjustment Factors
Cash-Dividend Total-Return Adjustment: From Price Drop to Exact Return
Builds a total-return series by reinvesting cash dividends at the ex-date.Corporate Actions and Security Master Data / Adjustment Factors
CRSP Cumulative Price Adjustment: Respect the Vendor Basis, Sign, and Gaps
The CRSP cumulative adjustment-factor convention, which is what academic finance means by an adjusted price.Corporate Actions and Security Master Data / Adjustment Factors
CRSP Cumulative Share/Volume Adjustment
The volume counterpart of the CRSP price adjustment. Volume moves the opposite way to price across a split, and adjusting one without the other silently corrupts every turnover and liquidity measure downstream.Corporate Actions and Security Master Data / Complex Distributions
Rights-Issue TERP Adjustment
Calculate TERP without confusing a methodology reference price with a traded ex-rights price.Corporate Actions and Security Master Data / Complex Distributions
Spin-Off Price Adjustment: Separate Parent Price from Distributed Value
Splits a parent's price history at a spin-off. One company becomes two, so the parent's own history must be restated by the value that left with the child — otherwise the parent shows a fall it never suffered.Corporate Actions and Security Master Data / Complex Distributions
Stock-Dividend Adjustment: Convert Price and Quantity Bases Without Inventing Value
Applies a stock dividend, where shareholders receive additional shares instead of cash.Corporate Actions and Security Master Data / Complex Distributions
Special-Dividend Adjustment: Preserve Return Meaning Across the Ex-Date
Handles a distribution large or irregular enough that treating it as an ordinary dividend misstates the series.Corporate Actions and Security Master Data / Complex Distributions
Return-of-Capital Adjustment: Keep Price, Return, and Tax Views Separate
Build a point-in-time capital-repayment factor without turning an index convention into a universal tax rule.Corporate Actions and Security Master Data / Identity Continuity
Permanent Security Identifier Mapping: Scoped, Effective-Dated Crosswalks
Resolves a vendor or exchange identifier to a permanent internal key.Corporate Actions and Security Master Data / Identity Continuity
Ticker-Change Chain Resolution
Follows a symbol through renames in either direction. FB became META, and any store keyed on the symbol now holds two disconnected halves of one company's history.Corporate Actions and Security Master Data / Identity Continuity
Share-Class Relationship Mapping: Same Issuer Does Not Mean Same Security
Relates share classes of one issuer — GOOG and GOOGL, voting and non-voting lines.Corporate Actions and Security Master Data / Identity Continuity
Merger Predecessor/Successor Mapping: Preserve Identity and Entitlements Without Inventing Continuity
Maps a position in a predecessor company onto what it became: successor shares, cash, or a mix.Corporate Actions and Security Master Data / Identity Continuity
Delisting Return Reconstruction: Separate Observed Proceeds from Estimates
Reconstructs the final return of a security that stopped trading.Corporate Actions and Security Master Data / Point-in-Time Universe
Historical Constituent Reconstruction: Rebuild the Roster Without Looking Ahead
Use effective time and knowledge time to reconstruct an index roster without today's constituents, later corrections, or silent gap filling.Corporate Actions and Security Master Data / Point-in-Time Universe
Survivorship-Bias Guard: Keep Historical Failures in the Test
Build a bitemporal universe guard that retains exited securities, rejects current-roster-only scopes, and separates membership from missing returns.Corporate Actions and Security Master Data / Point-in-Time Universe
IPO Availability Timestamping: Separate Listing Events from Research Knowledge
Decides when a newly listed security first became usable to research: whether every event type a named, versioned policy requires was effective for the evaluated instant and known by the research cutoff.Corporate Actions and Security Master Data / Point-in-Time Universe
Filing-Revision Versioning
Selects the version of a financial filing that was current at a knowledge time.Corporate Actions and Security Master Data / Point-in-Time Universe
Corporate-Action Status and Effective-Date Reconciliation
Reconstructs the highest-authority corporate-action state knowable at an as-of time while preserving conflicts and terminal messages.Index and Benchmark Engineering / Index Initialization and Continuity
Base-Date/Base-Value Initialization
Sets an index running: pick a base date and a base level, and the divisor follows from the market value on that date.Index and Benchmark Engineering / Index Initialization and Continuity
Index Divisor Initialization
The divisor itself: market value divided by the target level. Small, and the number every other calculation in this domain is defined against.Index and Benchmark Engineering / Index Initialization and Continuity
Divisor Continuity Adjustment
Rescales the divisor when market value changes for a non-market reason — a share issue, a member swap — so the level does not jump.Index and Benchmark Engineering / Index Initialization and Continuity
Corporate-Action Divisor Bridge
Applies a corporate action to an index by routing its non-market value change through the divisor.Index and Benchmark Engineering / Index Initialization and Continuity
Intraday Index-Level Calculation
Recomputes the level from a live price snapshot using fixed index shares and float factors.Index and Benchmark Engineering / Weighting and Capping
Price-Weighted Index
The Dow construction: sum the prices, divide by a divisor. Weight follows share *price*, not company size — a $500 stock moves it more than a $50 one ten times the size, which is why it tells a different story from the S&P.Index and Benchmark Engineering / Weighting and Capping
Total-Market-Cap Index
Weight by full market capitalisation. The textbook construction, and the starting point every float and capping rule modifies.Index and Benchmark Engineering / Weighting and Capping
Free-Float Market-Cap Index
Weight by the shares that can actually be bought. Excluding strategic, government and insider holdings is what makes an index replicable — a fund cannot buy shares that are not for sale.Index and Benchmark Engineering / Weighting and Capping
Capped Free-Float Market-Cap Index
Float weighting with a ceiling on any single constituent. Regulation and mandate limits require it, and the redistribution is subtler than it looks: capping one name lifts the others, which can push a second name over the cap.Index and Benchmark Engineering / Weighting and Capping
Modified Market-Cap Index
Applies an exponent to market value before weighting, compressing the gap between the largest and smallest members.Index and Benchmark Engineering / Weighting and Capping
Equal-Weight Index
Every constituent counts the same: each eligible name receives the target weight 1/N at the rebalance date.Index and Benchmark Engineering / Weighting and Capping
Iterative Cap Redistribution
The redistribution engine behind every capped index. Cap the offenders, spread the excess across the rest in proportion, repeat until nothing breaches — the loop is necessary because each pass can create new breaches.Index and Benchmark Engineering / Weighting and Capping
Group-Level Capping
Caps at two levels at once: each constituent, and each group it belongs to.Index and Benchmark Engineering / Alternative Weighting
Fundamental-Weighted Index
Weight by accounting size — sales, book value, cash flow, dividends — instead of market price.Index and Benchmark Engineering / Alternative Weighting
Dividend-Yield-Weighted Index
Weight by dividend yield. Straightforward arithmetic with a well-known failure mode: yield rises as price falls, so the construction naturally overweights companies in distress.Index and Benchmark Engineering / Alternative Weighting
Factor-Score-Weighted Index
Weight by a composite of factor scores — value, quality, momentum — with a floor so negative scores cannot produce negative weights.Index and Benchmark Engineering / Alternative Weighting
Minimum-Volatility Index
Solves for the weights that minimise portfolio variance for a given covariance matrix.Index and Benchmark Engineering / Alternative Weighting
Equal-Risk-Contribution Index
Risk parity: weights chosen so every constituent contributes the same share of total portfolio risk.Index and Benchmark Engineering / Alternative Weighting
Thematic-Tilt Index
Tilts a parent index toward a theme by scaling weights with a theme score, bounded so no single name runs away.Index and Benchmark Engineering / Return Variants
Price-Return Index
Level series from price returns alone, ignoring dividends. The number most often quoted, and the one that understates long-horizon performance.Index and Benchmark Engineering / Return Variants
Gross Total-Return Index
Reinvests dividends in full, with no tax deducted. The variant that assumes a holder who suffers no withholding — a domestic pension fund, typically.Index and Benchmark Engineering / Return Variants
Net Total-Return Index
Reinvests dividends after withholding tax. Over a decade the gap from the gross variant is large enough that quoting the wrong one materially misstates performance — and both are published under nearly the same name.Index and Benchmark Engineering / Return Variants
Excess-Return Index
Total return less a cash return, giving the return over funding.Index and Benchmark Engineering / Return Variants
Dividend-Point Index
Expresses dividends in index points rather than currency, which is how dividend futures and swaps are quoted.Index and Benchmark Engineering / Return Variants
Currency-Converted Index
Restates an index in another currency by compounding local returns with FX returns.Index and Benchmark Engineering / Return Variants
Currency-Hedged Index
Neutralises currency exposure with rolling forwards. Hedged and converted variants of the same index can diverge by double digits over a year — they are different products, not a formatting choice.Index and Benchmark Engineering / Strategy Indices
Leveraged Daily-Reset Index
Applies a leverage multiple that resets every day. Daily reset is why a 2× product does not deliver 2× over a month: in a choppy market, compounding the reset erodes the level even when the underlying ends flat.Index and Benchmark Engineering / Strategy Indices
Inverse Daily-Reset Index
An inverse multiple reset daily. The same path dependence as the leveraged case and in the same direction: over any period longer than a day, the result is not the negative of the underlying's return.Index and Benchmark Engineering / Strategy Indices
Volatility-Control Index
Scales exposure to hold realised volatility near a target, cutting it when markets get rough.Index and Benchmark Engineering / Strategy Indices
Fixed-Decrement Index
Deducts a fixed number of index points per year. Decrement indices exist to make option pricing on them cheaper, and the deduction is a real drag borne by the holder — not a fee schedule.Index and Benchmark Engineering / Strategy Indices
Percentage-Decrement Index
The same idea as a fixed decrement, but proportional to the level.Index and Benchmark Engineering / Strategy Indices
Index-of-Indices
Combines several index return streams into one under fixed weights.Index and Benchmark Engineering / Governance and Maintenance
Eligibility Screen
Applies the qualification rules that decide what may be considered for membership at all — domicile, listing status, share class, and the rest.Index and Benchmark Engineering / Governance and Maintenance
Liquidity Screen
Requires sustained tradability, not a single good month. The convention here is the median of the supplied monthly turnover ratios against a monthly threshold — a median monthly ratio, not an annualized traded value ratio.Index and Benchmark Engineering / Governance and Maintenance
Free-Float Factor Calculation
Derives the free-float factor from one aggregate restricted-share count, then rounds it up to a band. Classifying holdings into strategic, government, insider and cross-held categories is upstream work this function does not do.Index and Benchmark Engineering / Governance and Maintenance
IPO Fast-Entry Rule
Admits a large new listing between scheduled reviews. Without a fast-entry rule an index can spend months not holding one of the biggest companies in its own market.Index and Benchmark Engineering / Governance and Maintenance
Reconstitution Algorithm
Chooses the membership at a scheduled review, using an incumbent buffer so a name hovering at the boundary is not swapped in and out every period.Index and Benchmark Engineering / Governance and Maintenance
Rebalancing Algorithm
Turns a weight change into the trades that implement it, and reports the turnover.Index and Benchmark Engineering / Governance and Maintenance
Turnover Buffer Rule
The buffer in isolation: a band around the cutoff inside which incumbents keep their place.Index and Benchmark Engineering / Governance and Maintenance
Index Replication-Cost Estimator
Estimates what a rebalance costs to implement — spread, market impact and commission.Market Breadth and Internals / Advance/Decline Breadth
Net Advances: Count Participation Without Hiding Data Gaps
Build a revision-aware issue-count breadth snapshot that reconciles stable listings and refuses unsupported results.Market Breadth and Internals / Advance/Decline Breadth
Advance/Decline Ratio: Advancing Issues per Declining Issue
Calculate advancing issues per declining issue without hiding zero denominators, incomplete coverage, or correction timing.Market Breadth and Internals / Advance/Decline Breadth
Cumulative Advance/Decline Line: Recompute History Without Looking Ahead
Build a seeded, calendar-complete, revision-aware cumulative breadth line that refuses to publish incomplete evidence.Market Breadth and Internals / Advance/Decline Breadth
Normalized Advance/Decline Line: Cumulative (A-D)/(A+D) Breadth
Divides net advances by the number of issues traded before accumulating, which keeps the line comparable across decades as listing counts change.Market Breadth and Internals / Advance/Decline Breadth
Absolute Breadth Index
The absolute difference between advances and declines, in issues — direction discarded on purpose, and no interpretation of the magnitude claimed.Market Breadth and Internals / McClellan Family
Traditional McClellan Oscillator: Compare Fast and Slow Raw Breadth
The difference between a 19-day and a 39-day EMA of net advances.Market Breadth and Internals / McClellan Family
Ratio-Adjusted McClellan Oscillator
The McClellan oscillator computed on net advances divided by advances plus declines.Market Breadth and Internals / McClellan Family
Traditional McClellan Summation Index
The running total of the McClellan oscillator. Turns a fast, noisy signal into a slow regime gauge — the oscillator says what is happening this week, the summation index what has been happening for months.Market Breadth and Internals / McClellan Family
Ratio-Adjusted Summation Index (RASI)
RASI: the summation index built on the ratio-adjusted oscillator. The adjustment fixes the input scale; it does not make any threshold level universal.Market Breadth and Internals / McClellan Family
McClellan Volume Oscillator
The McClellan construction applied to advancing minus declining *volume* rather than issue counts. Divergence from the issue-count oscillator is out of scope here.Market Breadth and Internals / McClellan Family
McClellan Volume Summation Index
The running total of the volume oscillator — the volume-weighted counterpart of the summation index.Market Breadth and Internals / High/Low and Trend Breadth
New Highs–New Lows
Counts issues making new 52-week highs and lows. Unlike advance/decline it measures position against a long lookback rather than one session, so it detects a rally where fewer and fewer names reach new ground.Market Breadth and Internals / High/Low and Trend Breadth
High-Low Ratio
New highs as a share of new highs plus new lows — the scale-free form, comparable across universes and eras.Market Breadth and Internals / High/Low and Trend Breadth
High-Low Index
A moving average of the high–low ratio, which turns a noisy daily reading into something with a usable trend.Market Breadth and Internals / High/Low and Trend Breadth
Percent Above 20-Day MA
The share of the universe trading above its own 20-day moving average — a short-horizon participation gauge that turns over quickly.Market Breadth and Internals / High/Low and Trend Breadth
Percent Above 50-Day MA
The same participation measure over 50 sessions — the intermediate-horizon reading, and the one most often quoted for trend health.Market Breadth and Internals / High/Low and Trend Breadth
Percent Above 200-Day MA
Participation over 200 sessions — the long-horizon gauge. A rally with 80% of names above their 200-day average is a different market from one with 35%, even at the same index level.Market Breadth and Internals / Thrust and Pressure
Zweig Breadth Thrust
Detects the rare initiation signal: the advance ratio moving from below a low threshold to above a high one inside a bounded number of sessions.Market Breadth and Internals / Thrust and Pressure
Arms Index (TRIN)
TRIN: the advance/decline issue ratio divided by the advance/decline volume ratio.Market Breadth and Internals / Thrust and Pressure
Advance/Decline Volume Line
The cumulative line built from advancing minus declining volume rather than issue counts.Market Breadth and Internals / Thrust and Pressure
Upside/Downside Volume Ratio
Advancing volume over declining volume for one session. Extreme readings mark the days that matter — a 9-to-1 up day is a recognised initiation signal precisely because it is rare.Market Breadth and Internals / Thrust and Pressure
Cumulative TICK
Accumulates the net count of issues trading on an uptick versus a downtick.Market Breadth and Internals / Thrust and Pressure
Breadth-Divergence Detector
Flags sessions where the index and a breadth measure move meaningfully in opposite directions — the classic warning that an advance is being carried by fewer and fewer names.Market Breadth and Internals / Concentration and Diffusion
Top-N Index Contribution
How much of an index's move came from its largest N members. This is the arithmetic behind 'seven stocks are holding up the market' — a claim that is usually asserted and rarely measured.Market Breadth and Internals / Concentration and Diffusion
Herfindahl Constituent Concentration
The Herfindahl–Hirschman index of constituent weights: the sum of squared weights.Market Breadth and Internals / Concentration and Diffusion
Effective Number of Constituents
The reciprocal of HHI: how many equally weighted holdings would give the same concentration.Market Breadth and Internals / Concentration and Diffusion
Sector Diffusion Index
The share of sectors improving rather than deteriorating. Diffusion asks how *broad* a move is across groups, which a capitalisation-weighted index cannot show — one sector can carry the whole level.Market Breadth and Internals / Concentration and Diffusion
Factor Diffusion Index
The same diffusion measure across factors rather than sectors — momentum, size, volatility — showing whether a move is broad across styles or concentrated in one.Price Action and Candlesticks / Candle Foundations
Candle Anatomy
Decomposes one candle into body, upper and lower shadow, and direction.Price Action and Candlesticks / Candle Foundations
Scale-Aware Body Classification
Classifies a candle body as long, short or doji **relative to recent bodies** rather than against a fixed threshold.Price Action and Candlesticks / Candle Foundations
Shadow-to-Body Ratio
Decomposes one OHLC candle and reports raw and tick-stabilized shadow-to-body ratios without hiding the zero-body case.Price Action and Candlesticks / Candle Foundations
Gap Classification
Classifies full-range, body, or opening gaps in either direction using an explicit tick-scaled minimum distance.Price Action and Candlesticks / Candle Foundations
Trend-Context Filter
Classifies prior closes as an uptrend, downtrend, or sideways context from normalized net movement and path efficiency.Price Action and Candlesticks / Single-Candle Patterns
Doji
Evaluates one candle against the repository's explicit doji geometry and scale convention.Price Action and Candlesticks / Single-Candle Patterns
Dragonfly Doji
Evaluates one candle against the repository's explicit dragonfly-doji geometry and scale convention.Price Action and Candlesticks / Single-Candle Patterns
Gravestone Doji
Evaluates one candle against the repository's explicit gravestone-doji geometry and scale convention.Price Action and Candlesticks / Single-Candle Patterns
Marubozu
Evaluates one candle against the repository's explicit marubozu geometry and scale convention.Price Action and Candlesticks / Single-Candle Patterns
Spinning Top
Evaluates one candle against the repository's explicit spinning-top geometry and scale convention.Price Action and Candlesticks / Single-Candle Patterns
Hammer
Evaluates one candle against explicit hammer geometry, scale, and downtrend context conventions.Price Action and Candlesticks / Single-Candle Patterns
Hanging Man
Evaluates one candle against explicit hanging-man geometry, scale, and uptrend context conventions.Price Action and Candlesticks / Single-Candle Patterns
Inverted Hammer
Evaluates one candle against explicit inverted-hammer geometry, scale, and downtrend context conventions.Price Action and Candlesticks / Single-Candle Patterns
Shooting Star
Evaluates one candle against explicit shooting-star geometry, scale, and uptrend context conventions.Price Action and Candlesticks / Single-Candle Patterns
Long-Legged Doji
Marks each bar whose body is a small fraction of its high-low span while both shadows are long, and reports how much slack the tightest of those three tests had.Price Action and Candlesticks / Single-Candle Patterns
Four-Price Doji
Marks each bar whose entire range and whose open-to-close distance both sit within a tick tolerance, the degenerate candle where all four prices are effectively the same.Price Action and Candlesticks / Single-Candle Patterns
High-Wave Candle
Marks each bar with a small body relative to its high-low span whose two shadows are both a multiple of that body, the long-tailed indecision candle.Price Action and Candlesticks / Single-Candle Patterns
Belt Hold
Marks each bar that opens at one extreme of its own range within a tick and closes at least 60 percent of the span away, and reports that body share and which side it favoured.Price Action and Candlesticks / Two-Candle Patterns
Bullish Engulfing
Evaluates two candles against explicit bullish-engulfing geometry, scale, and downtrend context conventions.Price Action and Candlesticks / Two-Candle Patterns
Bearish Engulfing
Evaluates two candles against explicit bearish-engulfing geometry, scale, and uptrend context conventions.Price Action and Candlesticks / Two-Candle Patterns
Bullish Harami
Evaluates two candles against explicit bullish-harami containment, scale, and downtrend context conventions.Price Action and Candlesticks / Two-Candle Patterns
Bearish Harami
Evaluates two candles against explicit bearish-harami containment, scale, and uptrend context conventions.Price Action and Candlesticks / Two-Candle Patterns
Piercing Line
Evaluates two candles against explicit piercing-line gap, midpoint, scale, and downtrend conventions.Price Action and Candlesticks / Two-Candle Patterns
Dark Cloud Cover
Evaluates two candles against explicit dark-cloud gap, midpoint, scale, and uptrend conventions.Price Action and Candlesticks / Two-Candle Patterns
Tweezer Top
Evaluates two candles against explicit tweezer-top tolerance, rejection, scale, and uptrend conventions.Price Action and Candlesticks / Two-Candle Patterns
Tweezer Bottom
Evaluates two candles against explicit tweezer-bottom tolerance, rejection, scale, and downtrend conventions.Price Action and Candlesticks / Two-Candle Patterns
Harami Cross
Scans consecutive pairs of bars for a doji whose body sits inside the previous bar's body, and reports the pattern's direction from the colour of that earlier bar.Price Action and Candlesticks / Two-Candle Patterns
Kicking Pattern
Scans consecutive pairs of bars for two near-marubozu candles of opposite colour separated by a clean gap, with no overlap between the two ranges.Price Action and Candlesticks / Two-Candle Patterns
Matching Low
Scans consecutive pairs of bars for two down candles whose closes land within a tick of each other, marking a repeated closing floor.Price Action and Candlesticks / Two-Candle Patterns
Rising/Falling Window
Scans consecutive pairs of bars for a price gap, where the second bar's range clears the first bar's entirely in either direction.Price Action and Candlesticks / Multi-Candle Patterns
Morning Star
Evaluates exactly three candles against explicit morning-star gap, penetration, scale, and downtrend conventions.Price Action and Candlesticks / Multi-Candle Patterns
Evening Star
Evaluates exactly three candles against explicit evening-star gap, penetration, scale, and uptrend conventions.Price Action and Candlesticks / Multi-Candle Patterns
Three White Soldiers
Evaluates exactly three candles against explicit white-soldiers body, close, shadow, scale, and downtrend conventions.Price Action and Candlesticks / Multi-Candle Patterns
Three Black Crows
Evaluates exactly three candles against explicit black-crows body, close, shadow, scale, and uptrend conventions.Price Action and Candlesticks / Multi-Candle Patterns
Three Inside Up/Down
Evaluates exactly three candles against explicit inside-pair containment, confirmation, scale, and trend-context conventions.Price Action and Candlesticks / Multi-Candle Patterns
Three Outside Up/Down
Evaluates exactly three candles against explicit outside-pair engulfing, confirmation, scale, and trend-context conventions.Price Action and Candlesticks / Multi-Candle Patterns
Abandoned Baby
Evaluates exactly three candles against explicit abandoned-baby isolation, doji, penetration, scale, and context conventions.Price Action and Candlesticks / Multi-Candle Patterns
Morning Doji Star
Scans three-bar windows for a down candle, then a doji, then an up candle that closes above the midpoint of the first candle's body.Price Action and Candlesticks / Multi-Candle Patterns
Evening Doji Star
Scans three-bar windows for an up candle, then a doji, then a down candle that closes below the midpoint of the first candle's body.Price Action and Candlesticks / Multi-Candle Patterns
Three-Line Strike
Scans four-bar windows for three same-colour candles followed by one opposite candle whose body swallows the run from the first candle's body edge to the third's.Price Action and Candlesticks / Multi-Candle Patterns
Rising/Falling Three Methods
Scans five-bar windows for a long candle, three bars whose ranges stay inside it, and a fifth candle of the same colour that closes beyond the first one's close.Price Action and Candlesticks / Multi-Candle Patterns
Upside Gap Two Crows
Scans three-bar windows for an up candle, a gapped-up down candle, and a second down candle that opens higher still yet closes back inside the first candle's body.Price Action and Candlesticks / Multi-Candle Patterns
Mat Hold
Scans five-bar windows for an up candle, a gap above its close, three bars that hold above the first candle's body floor, and a fifth up candle closing above every high in the window so far.Price Action and Candlesticks / Candlestick Scanning and Context
Unified Candlestick Pattern Registry
construct a deterministic, versioned registry that rejects duplicate identities and ambiguous detector metadata.Price Action and Candlesticks / Candlestick Scanning and Context
Candlestick Pattern Occurrence Contract
normalize detector hits into reproducible occurrences with stable identity, causal timestamps, version, geometry score, and reason codes.Price Action and Candlesticks / Candlestick Scanning and Context
Market-Wide Candlestick Pattern Scanner
dispatch a frozen registry across injected detector candidates and emit only causal occurrence records with explicit rejection reasons.Price Action and Candlesticks / Candlestick Scanning and Context
Contextual Candlestick Confidence Score
combine available, direction-aligned evidence with explicit weights and a minimum evidence-coverage gate.Price Action and Candlesticks / Candlestick Scanning and Context
Support/Resistance Pattern Context
select the nearest causally confirmed directional level and turn ATR-normalized distance into a transparent [0,1] context feature.Price Action and Candlesticks / Candlestick Scanning and Context
Trend, Volatility, and Volume Pattern Context
derive three separately auditable context features from prior closes, ranges, and volumes plus the current closed bar.Price Action and Candlesticks / Candlestick Scanning and Context
Overlapping-Pattern Conflict Resolver
form connected overlap components and choose one reproducible winner using declared precedence and stable tie-breaks.Price Action and Candlesticks / Candlestick Scanning and Context
Candlestick Confirmation and Invalidation State Machine
advance directional candidates through closed-bar transitions with ordered levels, finite expiry, and complete reason-coded history.Price Action and Candlesticks / Candlestick Scanning and Context
Candlestick Scanner Ranking and Deduplication
calculate a traceable composite rank, keep deterministic order, and deduplicate only within an explicit identity key and bar window.Technical Indicators / Trend Smoothing
Simple Moving Average (SMA): Define the Window Before the Mean
Arithmetic mean of the last window observations, emitted at every position where a complete window is available.Technical Indicators / Trend Smoothing
Exponential Moving Average (EMA)
Exponentially weighted mean seeded with the simple mean of the first span observations, so the series is reproducible rather than dependent on where the data starts.Technical Indicators / Trend Smoothing
Weighted Moving Average (WMA): Newest-Heavy Linear Smoothing
Linearly weighted mean over window observations: the most recent observation carries weight window, the oldest weight 1.Technical Indicators / Trend Smoothing
Wilder RMA: SMA-Seeded Alpha 1/n Smoothing
Derive, implement, and verify an SMA-seeded Wilder moving average without hiding initialization or state.Technical Indicators / Trend Smoothing
Double Exponential Moving Average (DEMA): Reduced Lag and Overshoot
Double exponential moving average: 2 × EMA − EMA(EMA). Subtracting the second smoothing pass cancels most of the lag a single EMA introduces, at the cost of overshooting sharp reversals.Technical Indicators / Trend Smoothing
Triple Exponential Moving Average (TEMA): Layered Warm-Up and Signed Weights
Triple exponential moving average: 3 × EMA − 3 × EMA(EMA) + EMA(EMA(EMA)).Technical Indicators / Trend Smoothing
Hull MA
Hull moving average: a weighted combination of two WMAs de-lagged against each other, then re-smoothed over sqrt(window).Technical Indicators / Trend Smoothing
Kaufman Adaptive Moving Average (KAMA)
Learn KAMA step by step: efficiency ratio, squared smoothing constant, warm-up, code, edge cases, and an interactive 120-point lab.Technical Indicators / Trend Smoothing
MESA Adaptive Moving Average (MAMA)
A reproducible MAMA tutorial covering Hilbert phase, adaptive alpha, warm-up, Python and TypeScript, edge cases, and a 144-point laboratory.Technical Indicators / Trend Smoothing
Triangular Moving Average (TRIMA)
Smooths close twice with simple moving averages, an inner window of floor((period + 1) / 2) followed by an outer window of floor(period / 2) + 1, giving the triangular weighting its name.Technical Indicators / Trend Smoothing
Tillson T3 Moving Average
Chains six exponential moving averages of the same period over close and combines the third through sixth with the Tillson volume-factor coefficients, trading warm-up length for a smoother, less laggy curve.Technical Indicators / Trend Smoothing
Following Adaptive Moving Average (FAMA)
Runs an efficiency-ratio adaptive average over close and its slower follower: net movement across period bars divided by the summed absolute bar-to-bar movement sets the smoothing constant, and FAMA tracks MAMA at half that constant.Technical Indicators / Trend Smoothing
Arnaud Legoux Moving Average (ALMA)
Averages close under a Gaussian weight curve whose peak sits at offset * (period - 1) within the window and whose width is period / sigma, so pushing the offset toward 1 favours recent bars.Technical Indicators / Trend Smoothing
Fractal Adaptive Moving Average (FRAMA)
Estimates the fractal dimension of each period-bar close window by comparing the ranges of its two halves against the range of the whole, then smooths close with exp(-4.6 * (dimension - 1)) as the adaptive constant.Technical Indicators / Trend Smoothing
Zero-Lag Exponential Moving Average (ZLEMA)
Removes most of the EMA's lag by first de-lagging close into 2 * close[t] - close[t - lag], where lag is floor((period - 1) / 2), and then running an ordinary EMA of period over that adjusted series.Technical Indicators / Trend Smoothing
Least-Squares Moving Average (LSMA)
Fits an ordinary least-squares line to each period-bar window of close and reports the value of that line at the window's last bar, so the curve follows the local trend rather than its average.Technical Indicators / Trend Smoothing
Variable Index Dynamic Average (VIDYA)
Scales the EMA constant 2 / (period + 1) by the absolute Chande momentum oscillator of the last period one-bar changes, so the average speeds up in one-sided moves and nearly freezes when gains and losses balance.Technical Indicators / Trend Smoothing
McGinley Dynamic
Tracks close with McGinley's self-adjusting recursion, dividing the step toward the new close by k * period * (close / previous) ** 4 so the line accelerates when price runs away from it and coasts when price is near.Technical Indicators / Trend Smoothing
Jurik-Style Moving Average Design
Demonstrates the Jurik design idea without the proprietary internals: the current absolute bar-to-bar change is scored against its own period-bar average, and that score stretches a base smoothing constant between a floor and a ceiling before the…Technical Indicators / Trend Smoothing
Volume-Weighted Moving Average (VWMA)
Averages close over a rolling period-bar window using each bar's volume as its weight, so heavily traded bars pull the line further than quiet ones.Technical Indicators / Trend Smoothing
Quadratic-Weighted Moving Average
Averages close over a rolling period-bar window with weights that grow as the square of a bar's position, 1, 4, 9 and so on, front-loading recency harder than the linear weights of a WMA.Technical Indicators / Trend Smoothing
Gaussian Moving Average
Averages close under a Gaussian weight curve centred at offset * (period - 1) with width period / sigma.Technical Indicators / Trend Smoothing
Ehlers Super Smoother Filter
Applies Ehlers' two-pole Butterworth recursion to the two-bar mean of close, with feedback coefficients derived from period via exp(-sqrt(2) * pi / period), suppressing high-frequency noise with far less lag than a moving average of the same length.Technical Indicators / Trend Smoothing
Ehlers Instantaneous Trendline
Splits close into a smoothed centre line and what is left over: the trendline is an EMA of max(4, period) and the detrended series is the bar's close minus that trendline.Technical Indicators / Trend Systems
MACD: Read the Spreads Before You Read the Signals
Moving average convergence/divergence: the gap between a fast and a slow EMA, its own EMA as a signal line, and the difference between them as a histogram.Technical Indicators / Trend Systems
Percentage Price Oscillator (PPO): Normalize the MACD Spread
PPO divides the fast-minus-slow exponential moving-average spread by the slow EMA, turning a price-unit gap into a percentage. This makes the oscillator comparable across positive price scales while preserving the sign of the underlying EMA relationship.Technical Indicators / Trend Systems
Aroon Up, Down, and Oscillator: Measure Extreme Recency
Aroon measures how recently a rolling window produced its highest high and lowest low. It does not measure the distance price traveled; it maps the age of each extreme onto a 0–100 scale.Technical Indicators / Trend Systems
Directional Movement: From True Range to +DI, −DI, and DX
Wilder's Directional Movement system assigns each bar's winning outside move to +DM or −DM, normalizes smoothed movement by smoothed true range, and turns the separation between +DI and −DI into DX.Technical Indicators / Trend Systems
Average Directional Index (ADX): Smooth DX Without Inventing Direction
ADX is Wilder's recursive average of DX. It smooths the magnitude of +DI/−DI separation and therefore describes directional organization without saying whether the dominant side is up or down.Technical Indicators / Trend Systems
Ichimoku Cloud: Separate Range Midpoints from Plot-Time Displacement
Ichimoku combines rolling high-low midpoints with deliberate plotting displacement. The forward cloud contains values calculated from already observed data; the backward Chikou line is today's close drawn at an earlier chart coordinate.Technical Indicators / Trend Systems
Parabolic SAR: Audit the Stop, Extreme Point, and Acceleration Factor
Parabolic SAR projects a trailing stop toward the active trend's extreme point. Each strict new extreme raises the acceleration factor, while a price penetration reverses the state and resets acceleration.Technical Indicators / Trend Systems
Supertrend: Trace ATR Bands, Ratchets, and Direction Flips
Supertrend builds basic ATR bands around the bar midpoint, ratchets them with previous-band rules, and activates one band according to a recursive direction state.Technical Indicators / Trend Systems
Average Directional Index Rating (ADXR)
Runs the Wilder directional-movement system over the bars and returns the smoothed plus_di, minus_di and adx lines together with adxr, the average of the current adx and the adx from period bars earlier.Technical Indicators / Trend Systems
Vortex Indicator (+VI/−VI)
Sums the upward and downward vortex movements over a rolling window and divides each by the summed true range, giving the paired plus_vi and minus_vi lines.Technical Indicators / Trend Systems
Choppiness Index
Compares the summed true range over a window against the window's own high-to-low span, on a base-10 log scale normalised by the window length, so a trending stretch scores low and a choppy one scores high.Technical Indicators / Trend Systems
Trend Intensity Index
Splits each close into the part above and the part below a simple moving average, sums each part over a second window, and reports the upside sum as a percentage of the two sums combined.Technical Indicators / Trend Systems
QStick
Averages the candle body, close minus open, over a rolling window, so a positive reading means the window closed above its opens more often than not.Technical Indicators / Trend Systems
Mass Index
Takes the ratio of a 9-period EMA of the high-low range to the 9-period EMA of that EMA, then sums the ratio over a longer window, so range expansion after a contraction pushes the total up.Technical Indicators / Trend Systems
Vertical Horizontal Filter
Divides the highest-to-lowest close span over a window by the sum of the absolute bar-to-bar close changes in that same window, separating directed movement from back-and-forth movement.Technical Indicators / Trend Systems
Random Walk Index (High/Low)
Scores how far price has travelled against what a random walk would explain, by taking the largest displacement-over-expected-range ratio across every lookback length from 2 up to period, once upward and once downward.Technical Indicators / Trend Systems
Trend Trigger Factor
Compares the current window's high and low against the immediately prior window's, and reports the buy-minus-sell power as a percentage of their average.Technical Indicators / Trend Systems
Directional Trend Index
Wilder-smooths the net of the upward high moves against the downward low moves, and divides it by the smoothed total of both, giving a signed percentage that runs from -100 to 100.Technical Indicators / Trend Systems
Trend Strength Index
Measures the absolute gap between a fast and a slow EMA of the close in units of average true range, so the spread is comparable across volatility regimes.Technical Indicators / Momentum
Relative Strength Index (RSI)
Relative strength index: Wilder-smoothed average gain over average loss, mapped to 0–100.Technical Indicators / Momentum
Stochastic Oscillator
Where the close sits within the high–low range of the lookback, expressed as 0–100, then smoothed twice.Technical Indicators / Momentum
Stochastic RSI
The stochastic formula applied to RSI rather than to price — a second-order indicator that measures where RSI sits within its own recent range, and therefore moves far faster than either input.Technical Indicators / Momentum
Williams %R
Where the close sits within the lookback's high–low range, on a −100…0 scale.Technical Indicators / Momentum
Commodity Channel Index (CCI)
Commodity channel index: the typical price's distance from its moving average, scaled by mean absolute deviation.Technical Indicators / Momentum
Ultimate Oscillator
Weighted buying pressure across three lookbacks at once, which is what makes it less sensitive to the choice of any single period than a plain oscillator.Technical Indicators / Momentum
True Strength Index (TSI)
True strength index: price change smoothed twice, divided by absolute price change smoothed the same way.Technical Indicators / Momentum
Connors RSI
The average of three components: RSI of price, RSI of the up/down streak length, and the percentile rank of the latest return.Technical Indicators / Momentum
Absolute Price Oscillator
Subtracts a slow EMA of close from a fast EMA of close, leaving the momentum spread in price units rather than as a percentage.Technical Indicators / Momentum
Rate-of-Change Variants (ROC, ROCP, and ROCR)
Expresses the same period-bar price ratio three ways: as a percentage, as a proportion, and as the raw ratio.Technical Indicators / Momentum
Price Momentum (MOM)
The plain price difference between the current close and the close period bars earlier.Technical Indicators / Momentum
Chande Momentum Oscillator
Compares summed up-closes against summed down-closes over a period window and scales the imbalance to a -100..100 range.Technical Indicators / Momentum
Awesome Oscillator
Subtracts a 34-period simple average of the median price from a 5-period one, measuring the gap between short and long swing momentum.Technical Indicators / Momentum
Accelerator Oscillator
Subtracts a 5-period simple average of the Awesome Oscillator from the oscillator itself, isolating the change in momentum rather than its level.Technical Indicators / Momentum
TRIX
The one-bar percentage rate of change of a triple-smoothed EMA of close, which strips most short-cycle noise before measuring momentum.Technical Indicators / Momentum
Stochastic Momentum Index
Measures where close sits relative to the midpoint of the period high-low range, then double-smooths both the distance and the range before scaling to -100..100.Technical Indicators / Momentum
Relative Vigor Index
Divides the period average of the candle body by the period average of the candle range, reading closing vigour relative to the day's travel.Technical Indicators / Momentum
Relative Momentum Index
An RSI-shaped 0..100 reading built on the change over momentum_lag bars instead of the one-bar change, Wilder-smoothed over period.Technical Indicators / Momentum
Fisher Transform
Rescales close to its position within the period high-low range of closes, clamps it just inside -1..1, and applies the Fisher transform to give the result near-Gaussian tails.Technical Indicators / Momentum
Inverse Fisher Transform
Squashes a scaled one-bar close change into -1..1 with the inverse Fisher transform, which is the hyperbolic tangent of the scaled input.Technical Indicators / Momentum
Schaff Trend Cycle
Runs the MACD line through two stochastic passes, each followed by a 3-period EMA, turning a trend measure into a 0..100 cycle oscillator.Technical Indicators / Momentum
Quantitative Qualitative Estimation (QQE)
Smooths a Wilder RSI with a 5-period EMA and wraps it in a volatility band derived from a double Wilder-smoothed average of the smoothed RSI's own absolute change.Technical Indicators / Momentum
WaveTrend Oscillator
Builds a CCI-style channel index from the typical price against its own 10-period EMA and mean deviation, then smooths it into a fast line and a slower trigger.Technical Indicators / Momentum
Know Sure Thing (KST)
Weights four smoothed rate-of-change readings taken over different lookbacks into a single momentum line, with a simple-average signal.Technical Indicators / Momentum
Chande Forecast Oscillator
Fits a least-squares line to the last period closes and reports how far the actual close sits from that line's endpoint, as a percentage of price.Technical Indicators / Momentum
Detrended Price Oscillator
Removes the trend by subtracting the current period simple average from a close shifted back half that window, leaving the short cycle around the average.Technical Indicators / Momentum
Balance of Power
Divides each candle's body by its full range, giving a per-bar -1..1 reading of how much of the session's travel the close managed to keep.Technical Indicators / Momentum
Psychological Line
The percentage of the last period bars that closed above the previous close, a plain count of how one-sided recent sentiment has been.Technical Indicators / Momentum
Pretty Good Oscillator
Expresses the gap between close and its period simple average in units of average true range, so readings stay comparable across volatility regimes.Technical Indicators / Momentum
Price Momentum Oscillator
Smooths a heavily scaled one-bar rate of change through two successive EMAs, then adds a third EMA as the signal line.Technical Indicators / Volatility and Channels
True Range
The greater of today's range, the gap up from yesterday's close, and the gap down from it.Technical Indicators / Volatility and Channels
Average True Range (ATR)
Wilder-smoothed true range. Most often used for position sizing and stop placement rather than as a signal — it says how far price typically moves, not which way.Technical Indicators / Volatility and Channels
Bollinger Bands
A moving average with bands a number of standard deviations away, so the channel widens and narrows with realised volatility.Technical Indicators / Volatility and Channels
Keltner Channels
An EMA with bands placed a number of ATRs away. Because it scales with true range rather than standard deviation, it reacts differently to gaps than Bollinger Bands — which is the basis of the squeeze comparison between the two.Technical Indicators / Volatility and Channels
Donchian Channels
The highest high and lowest low of the lookback. The oldest channel in use, and the only one here with no smoothing at all — the bands step rather than glide.Technical Indicators / Volatility and Channels
Bollinger BandWidth
The width of a Bollinger channel relative to its middle band, in percent.Technical Indicators / Volume Indicators
On-Balance Volume (OBV)
On-balance volume: a running total that adds the bar's volume when price closed up and subtracts it when price closed down.Technical Indicators / Volume Indicators
Accumulation/Distribution Line
Weights each bar's volume by where the close sat within that bar's range, then accumulates.Technical Indicators / Volume Indicators
Chaikin Money Flow
Money-flow volume summed over a lookback and divided by total volume over the same window — the accumulation/distribution idea as a bounded oscillator rather than a running total.Technical Indicators / Volume Indicators
Money Flow Index
RSI computed on typical price weighted by volume — commonly described as volume-weighted RSI, and read on the same 0–100 scale.Technical Indicators / Volume Indicators
Volume Price Trend
Like OBV, but each bar contributes volume scaled by the size of the return rather than only its sign — so a 3% move counts for more than a 0.1% one.Technical Indicators / Volume Indicators
Force Index
Price change multiplied by volume, then smoothed. Combines direction, size and participation in one number — a large move on no volume scores low.Technical Indicators / Volume Indicators
Chaikin A/D Oscillator
Builds the cumulative accumulation/distribution line from the money flow multiplier and volume, then returns the difference between a fast and a slow EMA of that line.Technical Indicators / Volume Indicators
Session VWAP Indicator
Accumulates typical price times volume divided by cumulative volume, restarting the accumulation at every new session.Technical Indicators / Volume Indicators
Anchored VWAP
Accumulates typical price times volume divided by cumulative volume from a chosen anchor bar onward, with no session reset.Technical Indicators / Volume Indicators
Negative Volume Index
Tracks a cumulative index seeded at 1000 that compounds the close-to-close return only on bars whose volume fell against the prior bar.Technical Indicators / Volume Indicators
Positive Volume Index
Tracks a cumulative index seeded at 1000 that compounds the close-to-close return only on bars whose volume rose against the prior bar.Technical Indicators / Volume Indicators
Ease of Movement
Divides the typical-price change by a box ratio built from scaled volume over the bar range, then smooths that raw reading with a simple moving average.Technical Indicators / Volume Indicators
Klinger Volume Oscillator
Signs each bar's volume force by the direction of the high-low-close sum and weights it by where the close sits in the bar range, then returns the fast EMA of that force minus the slow EMA.Technical Indicators / Volume Indicators
Volume Oscillator
Returns the difference between a fast and a slow simple moving average of raw volume.Technical Indicators / Volume Indicators
Percentage Volume Oscillator
Expresses the gap between a fast and a slow EMA of volume as a percentage of the slow EMA.Technical Indicators / Volume Indicators
Volume Rate of Change
Measures the percentage change in volume against the bar period positions earlier.Technical Indicators / Volume Indicators
Relative Volume
Divides each bar's volume by the simple moving average of volume over the preceding window, giving a multiple of normal activity.Technical Indicators / Volume Indicators
Money Flow Multiplier and Money Flow Volume
Returns the per-bar money flow multiplier, the close's position within the bar range mapped to minus one through one, and that multiplier times volume.Technical Indicators / Volume Indicators
Volume-Weighted MACD
Runs the MACD construction on volume-weighted moving averages of close instead of exponential ones, and smooths the resulting line into a signal.Technical Indicators / Volume Indicators
Volume Zone Oscillator
Signs each bar's volume by the direction of the close change, then expresses the EMA of that signed volume as a percentage of the EMA of total volume.Technical Indicators / Volume Indicators
Twiggs Money Flow
Accumulates volume weighted by where the close sits inside a range extended to include the prior close, then divides the EMA of that flow by the EMA of volume.Technical Indicators / Range and Volatility Indicators
Normalized ATR and ATR Percentage
Wilder's Average True Range over period bars, and the same figure restated as a percentage of that bar's close.Technical Indicators / Range and Volatility Indicators
Chaikin Volatility
Chaikin Volatility: the percentage change, roc_period bars apart, in an exponential moving average of the bar's high-low range.Technical Indicators / Range and Volatility Indicators
Ulcer Index
Ulcer Index: the root mean square of the percentage drawdown from the running peak close, measured across a window of period bars.Technical Indicators / Range and Volatility Indicators
Relative Volatility Index
Relative Volatility Index: an RSI-shaped 0-100 oscillator that grades the rolling standard deviation of close recorded on up bars against the same measure recorded on down bars.Technical Indicators / Range and Volatility Indicators
Volatility Ratio
Volatility Ratio: the standard deviation of close-to-close simple returns over a short window divided by the same measure over a long window.Technical Indicators / Range and Volatility Indicators
Volatility Quality Index
Volatility Quality Index: accumulates each bar's true range signed by the direction of its close, then smooths the running total with an exponential moving average.Technical Indicators / Range and Volatility Indicators
Average Daily Range
Average Daily Range: the simple moving average of the bar's high-low range over period bars.Technical Indicators / Range and Volatility Indicators
Gap Volatility
Gap Volatility: measures each bar's opening gap -- this open less the prior close -- and the rolling standard deviation of those gaps.Technical Indicators / Range and Volatility Indicators
Range Efficiency Ratio
Range Efficiency Ratio: the absolute net close-to-close move across period bars divided by the sum of the high-low ranges over the same span.Technical Indicators / Range and Volatility Indicators
High-Low Range Percentage
Expresses the bar's high-low range as a percentage of its high-low midpoint: 200 * (high - low) / (high + low).Technical Indicators / Range and Volatility Indicators
Normalized Price Range
Places the close inside the highest high and lowest low of the last period bars, scaled to a 0-1 position.Technical Indicators / Range and Volatility Indicators
Volatility Stop
Volatility Stop: a trailing long stop set multiplier ATRs below the highest close of the last period bars, and a short stop the same distance above the lowest close.Technical Indicators / Bands, Envelopes, and Squeezes
Bollinger %B
Bollinger Bands together with %B, the close's position between the lower and upper band.Technical Indicators / Bands, Envelopes, and Squeezes
Moving Average Envelope
Moving Average Envelope: a simple moving average of close with bands set a fixed percentage above and below it.Technical Indicators / Bands, Envelopes, and Squeezes
ATR Bands
ATR Bands: a simple moving average of close with bands multiplier Average True Ranges above and below it.Technical Indicators / Bands, Envelopes, and Squeezes
Standard Deviation Channel
Standard Deviation Channel: a simple moving average of close with bands multiplier population standard deviations above and below it.Technical Indicators / Bands, Envelopes, and Squeezes
Regression Channel
Regression Channel: the end point of a rolling least-squares fit of close over period bars, with bands multiplier root-mean-square residuals above and below that fitted point.Technical Indicators / Bands, Envelopes, and Squeezes
Raff Regression Channel
Raff Regression Channel: the same rolling least-squares centre line as the regression channel, but the channel half-width is the largest absolute residual in the window rather than its root mean square.Technical Indicators / Bands, Envelopes, and Squeezes
STARC Bands
STARC Bands: a simple moving average of close with bands multiplier Average True Ranges above and below it.Technical Indicators / Bands, Envelopes, and Squeezes
Fractal Chaos Bands
Fractal Chaos Bands: carries forward the most recent confirmed five-bar fractal high and fractal low, each held flat until a new fractal of that side confirms.Technical Indicators / Bands, Envelopes, and Squeezes
Projection Bands
Projection Bands: fits a least-squares slope to the highs and to the lows of the last period bars, projects every bar in the window forward along that slope, and takes the highest projected high and the lowest projected low.Technical Indicators / Bands, Envelopes, and Squeezes
Dynamic Zone Bands
Dynamic Zone Bands: a quantile envelope of close -- the upper band is the 1 - q quantile of the last period closes and the lower band the q quantile -- drawn around a simple moving average.Technical Indicators / Bands, Envelopes, and Squeezes
TTM Squeeze
TTM Squeeze: flags the bars on which the Bollinger band pair sits entirely inside the Keltner channel pair, the conventional sign of a volatility contraction.Technical Indicators / Bands, Envelopes, and Squeezes
Squeeze Momentum
Squeeze Momentum: the TTM squeeze flag and its two band pairs, plus a momentum line -- the regression slope of the close's distance from the midpoint of the period-bar high-low range.Technical Indicators / Bands, Envelopes, and Squeezes
Adaptive Price Zone
Adaptive Price Zone: a double-smoothed EMA of close as the centre line, with bands multiplier double-smoothed EMAs of the high-low range above and below it.Technical Indicators / Price Transforms
Typical Price
Averages each bar's high, low and close into a single representative price.Technical Indicators / Price Transforms
Median Price Transform
Takes the midpoint of each bar's high and low.Technical Indicators / Price Transforms
Weighted Close
Averages high, low and a double-weighted close so the settlement price dominates the bar.Technical Indicators / Price Transforms
Average Price Transform
Averages all four OHLC prices into one value per bar.Technical Indicators / Price Transforms
Heikin-Ashi Transform
Rebuilds each bar as a Heikin-Ashi candle, averaging OHLC into the smoothed close and carrying the smoothed open forward from the previous candle.Technical Indicators / Price Transforms
Log Price Transform
Takes the natural logarithm of each close and the first difference of those logs.Technical Indicators / Price Transforms
Price Relative
Rebases the ratio of close to a benchmark level so the first bar equals base, producing a relative-strength line.Technical Indicators / Price Transforms
Normalized Price Transform
Converts close into a rolling z-score against its own moving average and standard deviation.Technical Indicators / Rolling Statistical Indicators
Rolling Percentile
Reports where the current close sits inside its own trailing window, as the percentage of window values below it plus a configurable share of the values equal to it.Technical Indicators / Rolling Statistical Indicators
Rolling Quantile
Returns the requested quantile of the close over a trailing window, sorting each window and interpolating linearly between the two neighbouring ranks.Technical Indicators / Rolling Statistical Indicators
Rolling Beta
Regresses the asset's simple returns on the benchmark's over a trailing window and returns the slope, using the population covariance and variance of the window.Technical Indicators / Rolling Statistical Indicators
Rolling Alpha
Runs the same trailing regression of asset returns on benchmark returns as rolling beta, and returns the intercept, the mean asset return left over after the beta-weighted mean benchmark return is removed.Geometric Chart Patterns / Pivots and Levels
Causal Pivot Detection
Learn to separate pivot event time from confirmation time and implement a detector that never sees future bars with formulas, synthetic fixtures, Python, TypeScript, visuals, and an interactive lab.Geometric Chart Patterns / Pivots and Levels
ZigZag Segmentation
Learn to build a causal percentage-reversal state machine with explicit confirmed and repaintable endpoints with formulas, synthetic fixtures, Python, TypeScript, visuals, and an interactive lab.Geometric Chart Patterns / Pivots and Levels
Support/Resistance Clustering
Learn to turn confirmed pivots into scale-aware level clusters with explicit noise and knowledge time with formulas, synthetic fixtures, Python, TypeScript, visuals, and an interactive lab.Geometric Chart Patterns / Pivots and Levels
Robust Trendline Fitting
Learn to fit deterministic support or resistance trendlines without letting one outlier dominate ordinary least squares with formulas, synthetic fixtures, Python, TypeScript, visuals, and an interactive lab.Geometric Chart Patterns / Pivots and Levels
Classic and Floor-Trader Pivot Points
Projects the classic floor-trader pivot and two resistance/support pairs for each bar from the previous bar's high, low, and close.Geometric Chart Patterns / Pivots and Levels
Fibonacci Pivot Points
Takes the same (H + L + C) / 3 pivot as the classic variant but places the bands at Fibonacci fractions of the previous bar's range: r1/s1 at 0.382 of it and r2/s2 at 0.618.Geometric Chart Patterns / Pivots and Levels
Camarilla Pivot Points
Anchors its bands on the previous bar's close rather than on the pivot: r1/s1 sit at close ± 1.1 × range / 12 and r2/s2 at close ± 1.1 × range / 6.Geometric Chart Patterns / Pivots and Levels
Woodie Pivot Points
Weights the current bar's open into the pivot, (H_prev + L_prev + 2 × open) / 4, then derives r1/s1 by reflecting that pivot across the previous low and high and r2/s2 by adding and subtracting the previous bar's range.Geometric Chart Patterns / Pivots and Levels
DeMark Pivot Points
Chooses one of three formulas for the intermediate X depending on whether the previous bar closed below, above, or level with its open, then reports pivot = X / 4 with a single band pair r1 = X / 2 - L_prev and s1 = X / 2 - H_prev.Geometric Chart Patterns / Pivots and Levels
Rolling Support and Resistance
Reports, for each bar, the lowest low and highest high of the period bars that came strictly before it.Geometric Chart Patterns / Pivots and Levels
Fractal Support and Resistance
Holds the most recent confirmed five-bar fractal high and low forward as resistance and support.Geometric Chart Patterns / Pivots and Levels
ATR Support and Resistance
Places support and resistance a volatility-scaled distance either side of a simple moving average of close: center ± multiplier × ATR(period), where the ATR is Wilder-smoothed true range.Geometric Chart Patterns / Pivots and Levels
Pivot Range Width
Measures the central pivot range rather than its bands: bottom is the previous bar's midpoint (H + L) / 2, top is that midpoint reflected through the pivot, and width is the absolute distance between them.Geometric Chart Patterns / Reversal Structures
Double Top
Double top detection: two comparable highs separated by a trough, confirmed on a close below the neckline.Geometric Chart Patterns / Reversal Structures
Double Bottom
Double bottom detection: two comparable lows separated by a peak, confirmed on a close above the neckline.Geometric Chart Patterns / Reversal Structures
Triple Top
Triple top detection: three comparable highs, confirmed on a close below the neckline.Geometric Chart Patterns / Reversal Structures
Triple Bottom
Triple bottom detection: three comparable lows, confirmed on a close above the neckline.Geometric Chart Patterns / Reversal Structures
Head and Shoulders
Head and shoulders detection: a central high flanked by two lower highs, confirmed on a close below the neckline.Geometric Chart Patterns / Reversal Structures
Inverse Head and Shoulders
Inverse head and shoulders detection: a central low flanked by two higher lows, confirmed on a close above the neckline.Geometric Chart Patterns / Continuation Structures
Ascending Triangle
Scans a close series for an ascending triangle - a flat ceiling sitting over a rising floor - and reports whether that shape is still forming, has broken out, or was rejected.Geometric Chart Patterns / Continuation Structures
Descending Triangle
Scans a close series for a descending triangle - a falling ceiling pressing down on a flat floor - and reports whether that shape is still forming, has broken out, or was rejected.Geometric Chart Patterns / Continuation Structures
Symmetrical Triangle
Scans a close series for a symmetrical triangle - a falling ceiling and a rising floor closing on each other - and reports whether that shape is still forming, has broken out, or was rejected.Geometric Chart Patterns / Continuation Structures
Flag
Scans a close series for a flag - a strong prior move followed by a narrow channel drifting against it - and reports whether that shape is still forming, has broken out, or was rejected.Geometric Chart Patterns / Continuation Structures
Pennant
Scans a close series for a pennant - a strong prior move followed by a small converging triangle - and reports whether that shape is still forming, has broken out, or was rejected.Geometric Chart Patterns / Continuation Structures
Rising/Falling Wedge
Scans a close series for a wedge - two boundaries tilted the same way while converging - and reports whether that shape is still forming, has broken out, or was rejected.Geometric Chart Patterns / Pattern Matching
Normalized Template Matching
Slides a template over a series and finds the window whose shape is closest to it.Geometric Chart Patterns / Pattern Matching
Dynamic-Time-Warping Pattern Match
Measures how far a query is from a candidate under dynamic time warping, which lets the two series stretch against each other in time instead of comparing them bar for bar.Geometric Chart Patterns / Pattern Matching
Matrix-Profile Motif Discovery
Computes the matrix profile of a series for a given subsequence length - for each window, the distance to its nearest non-overlapping neighbour - and reports the closest pair, the motif.Geometric Chart Patterns / Pattern Matching
Shapelet Pattern Classifier
Labels a series by how closely its best-matching window resembles a shapelet.Geometric Chart Patterns / Indicator Divergence Detection
Price–Indicator Pivot Alignment
Aligns confirmed price and indicator pivots of the same kind within an explicit lag bound while preserving both event and knowledge indexes.Geometric Chart Patterns / Indicator Divergence Detection
Regular Bullish/Bearish Divergence Detection
Detects regular bullish and bearish divergence from causally aligned consecutive pivot pairs.Geometric Chart Patterns / Indicator Divergence Detection
Hidden Bullish/Bearish Divergence Detection
Detects hidden bullish and bearish divergence from causally aligned consecutive pivot pairs.Geometric Chart Patterns / Indicator Divergence Detection
Multi-Indicator Divergence Adapters
Normalizes indicator pivots into one polarity- and scale-aware representation for downstream divergence logic.Geometric Chart Patterns / Indicator Divergence Detection
Divergence Strength and Quality Scoring
Scores the first detected divergence from explicit geometry, prominence, alignment, and separation components.Geometric Chart Patterns / Indicator Divergence Detection
Divergence Confirmation and Invalidation State Machine
Advances the first detected divergence through causal confirmation, invalidation, and expiry checks.Geometric Chart Patterns / Indicator Divergence Detection
Multi-Indicator Divergence Confluence
Combines same-geometry divergence events across distinct indicators using declared non-negative weights.Geometric Chart Patterns / Indicator Divergence Detection
Market-Wide Divergence Scanner and Ranking
Filters point-in-time eligible universe records and ranks them from explicit confluence, state, freshness, liquidity, and data-quality components.Geometric Chart Patterns / Level Confluence and Zone Scoring
Price-by-Volume Profile Construction
Aggregates eligible point-in-time trades into deterministic tick-aligned price-by-volume bins.Geometric Chart Patterns / Level Confluence and Zone Scoring
Point of Control, Value Area, HVN, and LVN Detection
Selects the point of control, expands a deterministic value area, and identifies local high- and low-volume nodes.Geometric Chart Patterns / Level Confluence and Zone Scoring
Fibonacci Retracement and Extension Projection
Projects declared retracement and extension ratios from a directed price leg and snaps every level to the nearest tick.Geometric Chart Patterns / Level Confluence and Zone Scoring
Psychological Round-Number Level Generation
Generates tick-aligned round-number levels inside explicit bounds and labels their salience and distance from current price.Geometric Chart Patterns / Level Confluence and Zone Scoring
Multi-Source Support/Resistance Zone Fusion
Clusters nearby levels, computes deterministic zone centers, and separates accepted multi-source zones from rejected clusters.Geometric Chart Patterns / Level Confluence and Zone Scoring
Support/Resistance Zone Strength and Decay Scoring
Scores zone strength from source confluence, decayed touches, rejection quality, durability, and break penalties.Geometric Chart Patterns / Level Confluence and Zone Scoring
Support/Resistance Role-Reversal State Machine
Processes closes through active-role, break, retest, confirmation, and invalidation transitions for one zone.Geometric Chart Patterns / Level Confluence and Zone Scoring
Breakout and Retest Detection
Processes bars through breakout-pending, retest, confirmation, failure, and expiry states around one zone.Geometric Chart Patterns / Level Confluence and Zone Scoring
Market-Wide Zone-Proximity Scanner and Ranking
Filters point-in-time zone records by proximity and ranks eligible instruments from proximity, strength, and freshness.Geometric Chart Patterns / Market Structure, Breakouts, and Regimes
Highest-High and Lowest-Low Primitives
The two rolling extremes every breakout rule is built on: the highest high and lowest low over a window of period bars ending at, and including, the current bar.Geometric Chart Patterns / Market Structure, Breakouts, and Regimes
Single-Asset New-High/New-Low Signal
Flags whether a single instrument's close has cleared the highest high or undercut the lowest low of the preceding period bars.Geometric Chart Patterns / Market Structure, Breakouts, and Regimes
Breakout Strength
Expresses how far a close sits beyond its Donchian channel in units of ATR, so a two-tick break in a quiet market and a two-tick break in a violent one do not score the same.Geometric Chart Patterns / Market Structure, Breakouts, and Regimes
Donchian Breakout
The Donchian channel over the preceding period bars plus the two breakout booleans it implies.Geometric Chart Patterns / Market Structure, Breakouts, and Regimes
Opening Range Breakout
Fixes the high and low of the session's first opening_bars bars and then tests every later close against that frozen range.Geometric Chart Patterns / Market Structure, Breakouts, and Regimes
Price Compression Index
Compares short-horizon volatility to long-horizon volatility as 100 × ATR(short_period) / ATR(long_period).Geometric Chart Patterns / Market Structure, Breakouts, and Regimes
Range Expansion Index
Scores directional conviction as the signed sum of close-to-close changes over period bars divided by the sum of their absolute values, scaled to ±100.Geometric Chart Patterns / Market Structure, Breakouts, and Regimes
Fractal Dimension Index
Compares the total path length walked by close over a window against the straight-line span of that window, on a log scale, and clamps the result to [1, 2].Geometric Chart Patterns / Market Structure, Breakouts, and Regimes
Hurst Exponent
A rolling rescaled-range estimate: over each window of period closes it takes the range of the mean-adjusted cumulative sum, divides by the window's standard deviation, and reports log(R/S) / log(period).Geometric Chart Patterns / Market Structure, Breakouts, and Regimes
Efficiency Ratio
Kaufman's ratio of net displacement to gross travel: the absolute change in close over period bars divided by the sum of the absolute bar-to-bar changes across the same span.Geometric Chart Patterns / Market Structure, Breakouts, and Regimes
Market Meanness Index
Counts how often close crosses the median of its own period-bar window and reports that as a percentage of the period - 1 opportunities.Geometric Chart Patterns / Market Structure, Breakouts, and Regimes
Trend/Range Regime Classifier
Labels each bar trend, range or uncertain by requiring two independent readings to agree: efficiency ratio at or above 0.55 with Choppiness at or below 45 gives trend, efficiency at or below 0.25 with Choppiness at or above 55 gives range, and…Geometric Chart Patterns / Market Structure, Breakouts, and Regimes
Volatility Regime Classifier
Computes realized volatility as the standard deviation of simple close returns over period bars, then ranks each reading against the last rank_period of them: bottom quartile is low, top quartile is high, everything between is normal.Geometric Chart Patterns / Market Structure, Breakouts, and Regimes
Directional Persistence
Maps each bar to +1, -1 or 0 by the sign of its close-to-close change, sums those signs over period bars, and reports the absolute total divided by period.Geometric Chart Patterns / Market Structure, Breakouts, and Regimes
Swing Structure Detector
Confirms five-bar swing highs and lows and labels each one against the previous swing of the same kind - HH, LH, HL, LL, or swing-high/swing-low for the first of each.Geometric Chart Patterns / Market Structure, Breakouts, and Regimes
Higher-High/Lower-Low Structure
Reduces price to the higher-high / lower-low sequence traders read structure from, labelling each confirmed five-bar swing HH, LH, HL or LL against the previous swing of its kind.Geometric Chart Patterns / Market Structure, Breakouts, and Regimes
Inside/Outside Bar Structure
Classifies each bar against its immediate predecessor as inside (high not above and low not below), outside (high not below and low not above), or neither.Geometric Chart Patterns / Market Structure, Breakouts, and Regimes
Market Entropy
Treats each bar as one of three states by the sign of its close change, then reports the Shannon entropy of the state distribution over a period-bar window, normalised by log(3) so a perfectly balanced mix scores 1.Statistical Time Series / Diagnostics
ACF
Autocorrelation at each lag. The first diagnostic to run on any series you intend to model: it shows whether there is structure to model at all, and slow decay is the classic signature of non-stationarity.Statistical Time Series / Diagnostics
PACF
Partial autocorrelation: correlation at each lag with the intervening lags removed.Statistical Time Series / Diagnostics
Augmented Dickey-Fuller
Tests for a unit root. The null is that the series *has* one — so failing to reject is not evidence of stationarity, merely absence of evidence against a unit root. That asymmetry is the most misread thing in applied time series.Statistical Time Series / Diagnostics
KPSS
Tests stationarity with the null *reversed* relative to ADF: here the null is that the series is stationary.Statistical Time Series / Diagnostics
Ljung-Box
Tests whether a group of autocorrelations is jointly zero. Applied to model residuals it answers the question that matters after fitting: is there structure left that the model failed to capture?Statistical Time Series / Diagnostics
Zivot-Andrews Break Test
A unit-root test that allows one structural break at an unknown date, found by searching.Statistical Time Series / Forecast Models
AutoReg
Forecasts from an autoregression with supplied coefficients. Estimation is deliberately separate: this evaluates a model you already have, which keeps the arithmetic checkable.Statistical Time Series / Forecast Models
ARMA
ARMA forecasting with supplied coefficients: autoregressive terms on past values, moving-average terms on past errors.Statistical Time Series / Forecast Models
ARIMA
ARMA on a differenced series, with forecasts integrated back to the original level.Statistical Time Series / Forecast Models
SARIMA/SARIMAX
Seasonal ARIMA with optional exogenous regressors. Future exogenous values must be supplied for the whole horizon — if you do not know them, the forecast is conditional on a guess, and that dependency is worth being explicit about.Statistical Time Series / Forecast Models
Holt-Winters
Additive Holt-Winters: exponential smoothing of level, trend and seasonality.Statistical Time Series / Forecast Models
Theta Forecast
The Theta method: decompose, extrapolate, recombine. It won the M3 forecasting competition and is roughly equivalent to simple exponential smoothing with drift — a useful benchmark precisely because it is so simple.Statistical Time Series / Multivariate Systems
VAR
Vector autoregression: every series regressed on lags of all of them.Statistical Time Series / Multivariate Systems
Structural VAR
Identifies structural shocks by Cholesky decomposition of the residual covariance.Statistical Time Series / Multivariate Systems
VECM
Vector error correction with a fixed cointegrating vector. For series that wander individually but not apart: differencing them separately would throw away the long-run relationship, which is usually the thing of interest.Statistical Time Series / Multivariate Systems
Impulse-Response Analysis
Traces how a one-off shock to one variable propagates through the system over time.Statistical Time Series / Multivariate Systems
Forecast-Error Variance Decomposition
Attributes each variable's forecast error variance to the structural shocks, by horizon.Statistical Time Series / State and Regime Models
Kalman Filter
Optimal recursive estimation of a hidden state from noisy observations in a linear Gaussian system.Statistical Time Series / State and Regime Models
Extended Kalman Filter
The Kalman filter for non-linear systems, linearised at each step.Statistical Time Series / State and Regime Models
Unscented Kalman Filter
Propagates a set of deterministically chosen sigma points through the non-linearity instead of linearising it.Statistical Time Series / State and Regime Models
Hidden Markov Model
Infers a discrete hidden regime from observations. Where the Kalman filter tracks a continuous state, this asks which of a small number of *regimes* the market is in — and returns a probability rather than a label.Statistical Time Series / State and Regime Models
Markov-Switching Autoregression
An autoregression whose coefficients switch with a hidden regime.Statistical Time Series / State and Regime Models
Bayesian Change-Point Detection
Online detection of structural breaks by tracking the posterior over run length — how long since the last change.Statistical Time Series / Decomposition and Cycles
STL Decomposition
Seasonal-trend decomposition by loess: splits a series into seasonal, trend and remainder.Statistical Time Series / Decomposition and Cycles
Hodrick-Prescott Filter
Separates trend from cycle by penalising trend curvature. Ubiquitous in macro and heavily criticised: it produces spurious cycles at the ends of the sample, so the most recent values — the ones you care about — are the least reliable.Statistical Time Series / Decomposition and Cycles
Baxter-King Filter
A band-pass filter isolating fluctuations between two periodicities.Statistical Time Series / Decomposition and Cycles
Christiano-Fitzgerald Filter
An asymmetric band-pass filter that uses the whole sample, so unlike Baxter-King it produces values at the ends.Statistical Time Series / Decomposition and Cycles
Fast Fourier Transform Periodogram
Estimates spectral power by frequency. Peaks suggest periodicity — but a trend leaks power across every frequency, which is why detrending is a parameter here rather than an afterthought.Statistical Time Series / Decomposition and Cycles
Wavelet Decomposition
Haar wavelet decomposition: splits the series into detail at successive scales plus a residual approximation.Statistical Time Series / Hilbert and Ehlers Cycle Analytics
Hilbert Transform Dominant Cycle Period
Estimates the dominant cycle length in bars from the bar-to-bar change in the Hilbert phase angle, clamping each raw estimate into the 6-to-50 bar range and smoothing it with a 0.2 / 0.8 exponential update.Statistical Time Series / Hilbert and Ehlers Cycle Analytics
Hilbert Transform Dominant Cycle Phase
Returns the instantaneous Hilbert phase angle in radians as atan2(quadrature, in_phase), where both components come from a four-tap filter over the residual of close against its 4-bar EMA.Statistical Time Series / Hilbert and Ehlers Cycle Analytics
Hilbert Transform Phasor Components
Exposes the raw phasor behind the Hilbert cycle family: the in-phase component, its quadrature partner from the four-tap filter, and the amplitude and angle they form.Statistical Time Series / Hilbert and Ehlers Cycle Analytics
Hilbert Transform SineWave
Turns the Hilbert phase angle into the classic sinewave pair, the sine of the phase and a lead sine shifted a quarter turn ahead, whose crossings are the usual cycle-turn signal.Statistical Time Series / Hilbert and Ehlers Cycle Analytics
Hilbert Transform Trend/Cycle Mode
Labels each bar trend or cycle by asking whether the distance from close to its exponential trend exceeds 1.5 times the current Hilbert phasor amplitude.Statistical Time Series / Hilbert and Ehlers Cycle Analytics
Ehlers Cyber Cycle
Runs close through a two-pole high-pass filter tuned to period, then smooths the residual with an EMA of the same span, leaving an oscillator centred on zero that tracks the shorter-than-period swings.Statistical Time Series / Hilbert and Ehlers Cycle Analytics
Ehlers Roofing Filter
Stacks the two halves of a roof: a two-pole high-pass filter tuned to period removes the slow drift, and an Ehlers Super Smoother run at half that span removes the fast noise, leaving the band in between.Statistical Time Series / Hilbert and Ehlers Cycle Analytics
Ehlers Decycler
Subtracts a two-pole high-pass residual from close, leaving a trend line with the sub-period wiggle removed and far less lag than a moving average of the same span.Volatility and Covariance / Historical Estimators
Close-to-Close Volatility
Observe a close shock enter and leave centered return dispersion.Volatility and Covariance / Historical Estimators
Parkinson Volatility
Change intraday range while keeping endpoint prices fixed.Volatility and Covariance / Historical Estimators
Garman-Klass Volatility
See the range term and body correction under valid OHLC geometry.Volatility and Covariance / Historical Estimators
Rogers-Satchell Volatility
Track the upper and lower log-distance products.Volatility and Covariance / Historical Estimators
Yang-Zhang Volatility
Separate overnight, weighted body and weighted range contributions.Volatility and Covariance / Realized Measures
Realized Variance
Identify which squared return dominates the measured variation.Volatility and Covariance / Realized Measures
Realized Covariance
Pair exact intervals, then inspect positive and negative products.Volatility and Covariance / Realized Measures
Bipower Variation
See how a shock affects its two adjacent absolute products.Volatility and Covariance / Realized Measures
Jump-Variation Detector
Separate the observed variation difference from its uncertainty and threshold.Volatility and Covariance / Realized Measures
Realized Kernel
Explain each weighted lag correction to realized variance.Volatility and Covariance / Conditional Volatility
ARCH
Follow a squared shock through a finite coefficient queue.Volatility and Covariance / Conditional Volatility
GARCH
Separate new shock information from carried variance.Volatility and Covariance / Conditional Volatility
EGARCH
Compare signed standardized shocks on the log-variance scale.Volatility and Covariance / Conditional Volatility
GJR-GARCH
Isolate the extra term activated by a negative lagged residual.Volatility and Covariance / Conditional Volatility
FIGARCH
Keep retained fractional weights and omitted backcast mass separate.Volatility and Covariance / Conditional Volatility
HAR-RV
Watch one elevated session enter and leave three overlapping horizons.Volatility and Covariance / Covariance Estimation
Sample Covariance
Add complete rows and audit sample means, denominator and cells.Volatility and Covariance / Covariance Estimation
EWMA Covariance
Watch the same new vector compete with the existing matrix.Volatility and Covariance / Covariance Estimation
Ledoit-Wolf Shrinkage
Compare estimated outer-product noise with target distance.Volatility and Covariance / Covariance Estimation
Oracle Approximating Shrinkage
Trace the finite-dimensional coefficient rather than assuming library equivalence.Volatility and Covariance / Covariance Estimation
Factor-Model Covariance
Change loadings, common-factor risk and specific risk independently.Volatility and Covariance / Covariance Estimation
Graphical-Lasso Covariance
Vary penalty independently from sample count and inspect precision edges.Market Microstructure / Trade Classification
Tick Test
Signs a trade buyer- or seller-initiated by comparing its price with the previous trade.Market Microstructure / Trade Classification
Quote Test
Signs a trade by which side of the prevailing midpoint it executed on.Market Microstructure / Trade Classification
Lee-Ready Trade Signing
The standard hybrid: quote test where the trade is away from the midpoint, tick test at it.Market Microstructure / Trade Classification
Bulk Volume Classification
Assigns a *fraction* of each volume bar to buyers rather than signing individual trades.Market Microstructure / Liquidity and Spreads
Quoted Spread
Ask minus bid — what the book advertises. The upper bound on what a small marketable order costs, and routinely wider than what trades actually pay.Market Microstructure / Liquidity and Spreads
Effective Spread
Twice the signed distance from the midpoint to the trade price — what the trade actually paid.Market Microstructure / Liquidity and Spreads
Realized Spread
The effective spread measured against the midpoint *after* a horizon, which strips out the permanent price impact and leaves what the liquidity provider actually earned.Market Microstructure / Liquidity and Spreads
Roll Spread Estimator
Infers the effective spread from the negative serial covariance of price changes alone — no quote data required.Market Microstructure / Liquidity and Spreads
Amihud Illiquidity Ratio
Average absolute return per unit of dollar volume — how much price moves per dollar traded.Market Microstructure / Liquidity and Spreads
Corwin-Schultz Spread Estimator
Estimates the spread from daily high-low ranges over two days, exploiting that the range reflects both volatility and spread while volatility scales with time and the spread does not.Market Microstructure / Order-Flow and Impact
Order Flow Imbalance
Net signed change in depth at the touch — the quantity that best explains short-horizon price moves in the microstructure literature.Market Microstructure / Order-Flow and Impact
Queue Imbalance
The share of depth resting on the bid versus the ask. A simple, strongly predictive feature for the direction of the next price move at very short horizons.Market Microstructure / Order-Flow and Impact
Kyle Lambda
The price-impact coefficient from regressing price change on signed order flow.Market Microstructure / Order-Flow and Impact
Hasbrouck Price Impact
Estimates a flow-first VAR(1) and sums its midpoint-return impulse response to a one-unit signed-flow shock.Market Microstructure / Order-Flow and Impact
PIN
Probability of informed trading, estimated by maximum likelihood on daily buy and sell counts.Market Microstructure / Order-Flow and Impact
VPIN
Volume-synchronised probability of informed trading: order imbalance measured in volume buckets rather than clock time.Market Microstructure / Order-Book Dynamics
Order-Book Slope
How steeply depth accumulates as you move away from the touch.Market Microstructure / Order-Book Dynamics
Depth-Weighted Midprice
A midpoint weighted by depth across several levels rather than the naive average of best bid and ask.Market Microstructure / Order-Book Dynamics
Microprice
The midpoint weighted by the *opposite* side's size, so a heavy bid pulls the price up.Market Microstructure / Order-Book Dynamics
Order-Book Resiliency
How quickly the book refills after being depleted, fitted as a decay over observed displacement.Market Microstructure / Order-Book Dynamics
Hawkes Order-Arrival Model
A self-exciting point process: each arrival raises the probability of the next.Market Microstructure / Market-Depth Analytics
Cumulative Bid/Ask Depth
Running total of quantity available as you walk out from the touch on each side — the basis of every question about how much can be traded before price moves.Market Microstructure / Market-Depth Analytics
Top-N Depth Imbalance
Depth imbalance restricted to the top N levels — the same idea as queue imbalance, bounded to the part of the book that is realistically accessible.Market Microstructure / Market-Depth Analytics
Depth-at-Distance Profile
Depth bucketed by distance from the touch, in ticks. Shows where liquidity actually sits rather than reducing the book to a single number.Market Microstructure / Market-Depth Analytics
Expected Market-Order Fill Price
Walks a market order through the book and returns the volume-weighted price it would pay.Market Microstructure / Market-Depth Analytics
Multi-Level Sweep Cost and Slippage
The cost of sweeping multiple levels, measured against a chosen benchmark.Market Microstructure / Market-Depth Analytics
Liquidity-Wall and Concentration Detection
Finds levels holding disproportionate size — the 'walls' that act as short-term barriers.Market Microstructure / Market-Depth Analytics
Depth Depletion and Replenishment
Separates a visible-depth quantity series into gross depletion and gross replenishment.Market Microstructure / Market-Depth Analytics
Market-Depth Heatmap Aggregation
Aggregates a sequence of book snapshots into a time-by-price grid — the data behind a depth heatmap, where persistent liquidity and fleeting quotes look completely different.Matching Engines and Venue Logic / Continuous Matching
Price-Time Priority
Matches an incoming order against resting orders by best price, then earliest arrival.Matching Engines and Venue Logic / Continuous Matching
Pro-Rata Matching
Allocates a fill across all resting orders at a price in proportion to size, ignoring arrival time.Matching Engines and Venue Logic / Continuous Matching
Size-Time Priority
Orders by size first and arrival second — rewarding large resting orders.Matching Engines and Venue Logic / Continuous Matching
Hybrid Pro-Rata/Time Matching
Splits an incoming order between a time-priority portion and a pro-rata portion — the compromise most futures venues actually run, because pure pro-rata invites size inflation and pure price-time invites a latency race.Matching Engines and Venue Logic / Auctions
Maximum-Executable-Volume Auction
Finds the price that crosses the most volume — the first and most important auction criterion.Matching Engines and Venue Logic / Auctions
Minimum-Imbalance Tie-Break
Applies the second auction criterion: among prices crossing equal volume, choose the one leaving the least unfilled imbalance.Matching Engines and Venue Logic / Auctions
Opening-Cross Price
Runs the full opening auction: maximum volume, minimum imbalance, then reference-price proximity, bounded by the permitted price range.Matching Engines and Venue Logic / Auctions
Closing-Cross Price
The closing auction, which sets the price index funds actually trade at.Matching Engines and Venue Logic / Auctions
Volatility-Auction Reopening
Classifies a volatility-auction reopening from scalar corridor state: continuous, no-cross, reopened, or extended.Matching Engines and Venue Logic / Order Controls
Tick-Size Validation
Rejects a price that is not a whole multiple of the instrument's tick.Matching Engines and Venue Logic / Order Controls
Price-Band Validation
Checks a limit price against the venue's dynamic price band. Bands move with the reference price, so a valid order becomes invalid moments later — which is why the band's as-of time is part of the check.Matching Engines and Venue Logic / Order Controls
Self-Trade Prevention
Stops a participant trading with itself — required by most venues, and the *mode* determines who loses their order.Matching Engines and Venue Logic / Order Controls
Cancel-on-Disconnect
Decides which orders to pull when a session drops. Not every disconnect should cancel — a deliberate logout and a network failure are different events, and cancelling a hedge because of a brief blip is its own risk.Matching Engines and Venue Logic / Order Controls
Fat-Finger Limit
Blocks obviously erroneous orders on quantity, notional and aggressive price deviation.Matching Engines and Venue Logic / Order Controls
Circuit-Breaker Trigger
Evaluates market-wide circuit breaker levels against the index move.Matching Engines and Venue Logic / Order Lifecycle and Queue State
Limit-Order Lifecycle State Machine
Replays an order's events into its state history — new, partially filled, replaced, cancelled, done.Matching Engines and Venue Logic / Order Lifecycle and Queue State
Cancel/Replace Priority Rule
Decides whether an amendment keeps queue position. Reducing quantity usually keeps it; raising quantity or changing price loses it. This one rule determines whether an amend is nearly free or extremely expensive.Matching Engines and Venue Logic / Order Lifecycle and Queue State
Partial-Fill and Residual-Quantity Processing
Tracks cumulative fills against an order and computes the residual.Matching Engines and Venue Logic / Order Lifecycle and Queue State
Queue Position and Ahead-Volume Calculation
How much volume sits ahead of a given order at its price. This is the number that decides fill probability under price-time priority — position in the queue, not distance from the touch.Matching Engines and Venue Logic / Order Lifecycle and Queue State
Iceberg/Reserve-Order Replenishment
Manages a hidden reserve that refills the displayed quantity as it fills.Matching Engines and Venue Logic / Order Lifecycle and Queue State
Marketable-Order Multi-Level Sweep
Walks a marketable order across price levels until filled or exhausted — the matching-engine counterpart of the expected-fill-price calculation, producing actual fills rather than an estimate.Execution and Transaction Cost Analysis / Schedule-Based Execution
TWAP Execution
Splits an order into equal slices across equal time buckets. The simplest schedule and the most predictable — predictable enough that it can be detected and traded against, which is the argument for the volume-based alternatives.Execution and Transaction Cost Analysis / Schedule-Based Execution
Historical VWAP Execution
Distributes an order according to a historical intraday volume profile — heavier at the open and close.Execution and Transaction Cost Analysis / Schedule-Based Execution
Adaptive VWAP Execution
Re-plans the remaining schedule from realised volume so far plus a forecast of what is left.Execution and Transaction Cost Analysis / Schedule-Based Execution
Percentage-of-Volume Execution
Trades a fixed share of whatever volume occurs. The schedule is unknown in advance by design, which limits impact — and means the order may not complete at all if volume never arrives.Execution and Transaction Cost Analysis / Cost/Risk Optimization
Almgren-Chriss Optimal Execution
The canonical optimal execution trajectory: trades off market impact against the risk of holding the position longer.Execution and Transaction Cost Analysis / Cost/Risk Optimization
Implementation-Shortfall Execution
Minimises total shortfall against the arrival price, including the opportunity cost of quantity that never executes.Execution and Transaction Cost Analysis / Cost/Risk Optimization
Arrival-Price Execution
Benchmarks against the price at the moment the decision was made, which front-loads execution.Execution and Transaction Cost Analysis / Cost/Risk Optimization
Liquidity-Seeking Execution
Trades opportunistically when liquidity appears rather than on a schedule.Execution and Transaction Cost Analysis / Cost/Risk Optimization
Opportunistic Dark-Pool Execution
Decides how much of an order to expose to each dark opportunity by applying firm-probability, price-improvement, minimum-size, cap and fallback gates in a fixed order.Portfolio Construction / Mean-Risk Optimization
Markowitz Mean-Variance
Solves for the lowest-variance asset weights that still meet a declared return target, from expected returns and a covariance matrix.Portfolio Construction / Mean-Risk Optimization
Global Minimum Variance
Computes the lowest-variance weights obtainable from a covariance matrix alone, with no expected-return input, and shows why clipping a short weight is not optimization.Portfolio Construction / Mean-Risk Optimization
Maximum Sharpe Ratio
Finds the weights that maximize the Sharpe ratio for a declared risk-free return, with the benchmark, horizon and volatility denominator stated rather than implied.Portfolio Construction / Mean-Risk Optimization
Mean-CVaR Optimization
Optimizes a portfolio against conditional value at risk over a discrete scenario set, including the partial tail mass a discrete distribution creates at the confidence level.Portfolio Construction / Mean-Risk Optimization
Mean-Absolute-Deviation Optimization
Minimizes mean absolute deviation subject to a return target by solving the linear program the absolute value reduces to, over a discrete scenario set.Portfolio Construction / Risk Allocation
Inverse-Volatility Weighting
Assigns capital in inverse proportion to each asset standalone volatility and normalizes the scores, with a covariance diagnostic showing what the rule leaves out.Portfolio Construction / Risk Allocation
Equal Risk Contribution
Solves for the weights that give every asset the same contribution to portfolio volatility, which equal capital weights do not.Portfolio Construction / Risk Allocation
Risk Budgeting
Solves for weights whose risk contributions match a declared budget per asset, generalizing equal risk contribution to unequal targets.Portfolio Construction / Risk Allocation
Hierarchical Risk Parity
Allocates capital by clustering assets on a correlation-derived profile distance, then splitting capital down the tree by branch variance, without inverting the covariance matrix.Portfolio Construction / Risk Allocation
Hierarchical Equal Risk Contribution
Combines hierarchical clustering with equal risk contribution, and makes the cluster-count stopping decision explicit instead of leaving it implicit.Portfolio Construction / Bayesian and Robust Allocation
Black-Litterman
Combines market-implied equilibrium returns with stated views and their confidence, producing the posterior expected returns an optimizer then uses.Portfolio Construction / Bayesian and Robust Allocation
Resampled Efficient Frontier
Averages optimizer weights across seeded bootstrap resamples at matching return rank, so the reported allocation reflects estimation noise rather than one sample.Portfolio Construction / Bayesian and Robust Allocation
Robust Mean-Variance
Optimizes against an explicit ellipsoidal uncertainty set around the mean, so the robustness claim names the uncertainty it is built to survive.Portfolio Construction / Bayesian and Robust Allocation
Distributionally Robust Portfolio
Minimizes the worst-case probability of a loss across every distribution sharing a given mean and covariance, subject to a return floor.Portfolio Construction / Bayesian and Robust Allocation
Kelly Allocation
Maximizes expected logarithmic growth over a discrete scenario set, separating the long-run growth criterion from the single-coin-toss intuition.Portfolio Construction / Practical Constraints
Turnover-Constrained Optimization
A production-minded guide to Turnover-Constrained Optimization.Portfolio Construction / Practical Constraints
Transaction-Cost-Aware Optimization
A production-minded guide to Transaction-Cost-Aware Optimization.Portfolio Construction / Practical Constraints
Cardinality-Constrained Portfolio
A production-minded guide to Cardinality-Constrained Portfolio.Portfolio Construction / Practical Constraints
Long/Short Gross-Net Constraints
Computes long, short, net, and gross exposure from signed weights, checks a net interval and gross cap, and solves the mean-variance problem under both.Portfolio Construction / Practical Constraints
Tax-Aware Portfolio Optimization
Scores which lots a fixed-size sale draws on, and separately solves the exact trade balancing return, tracking risk, cost and a declared illustrative lot score.Factor Investing and Asset Pricing / Asset-Pricing Models
CAPM Beta
Measure how much of an asset's historical excess return moves with the market and separate that slope from unexplained return.Factor Investing and Asset Pricing / Asset-Pricing Models
Fama-French Three-Factor Model
Separate market, size and value exposure before describing a return intercept as unexplained performance.Factor Investing and Asset Pricing / Asset-Pricing Models
Carhart Four-Factor Model
Identify whether a persistent-return strategy carries momentum exposure after accounting for market, size and value.Factor Investing and Asset Pricing / Asset-Pricing Models
Fama-French Five-Factor Model
Attribute returns to market, size, value, profitability and investment while keeping factor-definition changes visible.Factor Investing and Asset Pricing / Asset-Pricing Models
Arbitrage Pricing Theory
Calculate the return implied by supplied factor exposures and premia, and identify the assumption behind any apparent pricing gap.Factor Investing and Asset Pricing / Cross-Sectional Factors
Value Factor Score
Rank positive-book-equity companies by book-to-market without disguising invalid accounting denominators as cheapness.Factor Investing and Asset Pricing / Cross-Sectional Factors
Size Factor Score
Express a small-company tilt consistently across a market-cap distribution that spans orders of magnitude.Factor Investing and Asset Pricing / Cross-Sectional Factors
Momentum Factor Score
Build a prior-return score with an explicit formation date and skipped recent month.Factor Investing and Asset Pricing / Cross-Sectional Factors
Quality Factor Score
Combine profitability, leverage and earnings stability without confusing a broad quality score with one accounting ratio.Factor Investing and Asset Pricing / Cross-Sectional Factors
Low-Volatility Factor Score
Rank lower historical total-return variability while showing the lookback and annualization that define it.Factor Investing and Asset Pricing / Cross-Sectional Factors
Profitability Factor Score
Measure gross profit generated per unit of assets and distinguish it from other profitability definitions.Factor Investing and Asset Pricing / Factor Construction
Quantile Portfolio Sort
Turn a cross-sectional score into reproducible portfolios with transparent tie and remainder policies.Factor Investing and Asset Pricing / Factor Construction
Z-Score Composite Factor
Combine comparable factor scores while making scale, direction, missingness and weight choices visible.Factor Investing and Asset Pricing / Factor Construction
Sector-Neutral Factor
Remove sector-level score averages and verify which kind of neutrality the result actually achieves.Factor Investing and Asset Pricing / Factor Construction
Beta-Neutral Factor
Construct signal-derived weights with zero net exposure and zero exposure to a supplied beta vector.Factor Investing and Asset Pricing / Factor Construction
Residualized Factor
Extract the part of a cross-sectional signal that is linearly unexplained by specified control characteristics.Factor Investing and Asset Pricing / Factor Construction
Winsorized Rank Factor
Limit extreme characteristic values while preserving an explicit percentile and tied-rank policy.Factor Investing and Asset Pricing / Factor Evaluation
Information Coefficient
Measure linear cross-sectional association between a formed signal and subsequent returns without leaking labels into formation.Factor Investing and Asset Pricing / Factor Evaluation
Rank Information Coefficient
Evaluate whether signal ordering matches future-return ordering, including exact ties.Factor Investing and Asset Pricing / Factor Evaluation
Factor Turnover
Measure actual rebalance trading after portfolio drift, including entries, exits and the cash leg.Factor Investing and Asset Pricing / Factor Evaluation
Quantile Spread Return
Calculate a high-minus-low portfolio return and state exactly how gross exposure and cost accounting scale it.Factor Investing and Asset Pricing / Factor Evaluation
Factor Decay Curve
Trace how a frozen signal's association changes across fully matured forward horizons without confusing cumulative and incremental effects.Factor Investing and Asset Pricing / Market Efficiency and Behavioral Dynamics
Variance-Ratio Random-Walk Test
Test whether the variance of aggregated log returns scales as a random-walk benchmark predicts.Factor Investing and Asset Pricing / Market Efficiency and Behavioral Dynamics
Runs Test for Return Independence
Detect unusually clustered or alternating return signs while preserving an exact small-sample reference.Factor Investing and Asset Pricing / Market Efficiency and Behavioral Dynamics
Martingale-Difference Dependence Tests
Screen a claimed zero-conditional-mean innovation against both linear and nonlinear past information.Factor Investing and Asset Pricing / Market Efficiency and Behavioral Dynamics
Momentum and Reversal Horizon Decomposition
Separate recent, intermediate and distant return history without double-counting months or mistaking a chosen sign for evidence of reversal.Factor Investing and Asset Pricing / Market Efficiency and Behavioral Dynamics
Cross-Sectional Herding Detection
Estimate whether cross-sectional return dispersion bends downward during larger market moves, with uncertainty and interpretation limits.Factor Investing and Asset Pricing / Market Efficiency and Behavioral Dynamics
Overreaction and Underreaction Event Analysis
Trace abnormal returns around a predeclared event while keeping the estimation window and event window separate.Factor Investing and Asset Pricing / Market Efficiency and Behavioral Dynamics
Extrapolative-Expectations Proxy Construction
Build an explicit recent-return extrapolation proxy and identify what additional evidence would be needed to call it investor expectations.Factor Investing and Asset Pricing / Market Efficiency and Behavioral Dynamics
Adaptive-Markets Predictability Stability Test
Check whether a predeclared lag-return relationship changes across a fixed split, while distinguishing instability from proof of a market theory.Fundamental Analysis and Valuation / Statement Ratios
DuPont Decomposition
Decompose ROE into a multiplication identity that reconciles exactly and makes denominator alignment auditable.Fundamental Analysis and Valuation / Statement Ratios
ROIC Calculation
Build an explicit NOPAT and average-invested-capital bridge, then refuse false comparability across other ROIC conventions.Fundamental Analysis and Valuation / Statement Ratios
Cash Conversion Cycle
Calculate DIO, DSO, DPO, and CCC with average balances, aligned flows, explicit day count, and a visible DPO-denominator choice.Fundamental Analysis and Valuation / Statement Ratios
Interest-Coverage Ratio
Calculate times-interest-earned without netting interest income or importing a universal distress threshold.Fundamental Analysis and Valuation / Statement Ratios
Net-Debt/EBITDA
Reconcile every debt, cash, lease, interest, tax, and D&A component before interpreting a net-leverage multiple.Fundamental Analysis and Valuation / Statement Ratios
Common-Size Statements
Normalize a dense multi-period statement while preserving signs, row mappings, point-in-time versus period bases, and percentage-point changes.Fundamental Analysis and Valuation / Intrinsic Valuation
Free-Cash-Flow DCF
Build an auditable FCFF DCF that exposes every discount factor, terminal-value dependency, and enterprise-to-equity bridge item.Fundamental Analysis and Valuation / Intrinsic Valuation
Dividend Discount Model
Separate finite-stage dividend payments from the terminal dividend so timing and payout assumptions remain visible.Fundamental Analysis and Valuation / Intrinsic Valuation
Gordon Growth Model
Make the deceptively compact Gordon formula safe by freezing dividend timing and exposing the discount-growth spread.Fundamental Analysis and Valuation / Intrinsic Valuation
Residual-Income Model
Reconcile book-value roll-forwards, equity charges, residual income, and continuing value in one per-share audit trail.Fundamental Analysis and Valuation / Intrinsic Valuation
Economic Value Added
Connect NOPAT, invested capital, ROIC spread, EVA, market value added, and enterprise value without mixing equity and enterprise claims.Fundamental Analysis and Valuation / Relative Valuation
P/E Comparable Valuation
Build an auditable P/E comparable valuation that exposes every peer multiple, the median selection, dispersion, and the target-price bridge.Fundamental Analysis and Valuation / Relative Valuation
EV/EBITDA Comparable Valuation
Keep the enterprise multiple and equity-value bridge separate so debt, cash, preferred equity, NCI, nonoperating assets, and shares remain auditable.Fundamental Analysis and Valuation / Relative Valuation
Price-to-Book Valuation
Connect accounting equity to market equity without pretending book value is fair value or silently changing to tangible book.Fundamental Analysis and Valuation / Relative Valuation
PEG Ratio
Make the PEG unit trap, forecast vintage, zero-growth boundary, and limited economic interpretation impossible to miss.Fundamental Analysis and Valuation / Relative Valuation
Peer-Multiple Regression
Fit and audit a log-multiple OLS model with a frozen feature order, rank checks, residual diagnostics, and a target-value bridge.Fundamental Analysis and Valuation / Quality and Distress
Altman Z-Score
Build and audit the original five-factor Altman score without silently substituting Z-prime, Z-double-prime, or a modern probability of default.Fundamental Analysis and Valuation / Quality and Distress
Piotroski F-Score
Calculate every binary signal, show its evidence, and aggregate the original 0-to-9 F-Score without converting it into a universal quality rating.Fundamental Analysis and Valuation / Quality and Distress
Beneish M-Score
Reconstruct DSRI through TATA, reconcile every coefficient, and treat the M-Score as an investigation trigger rather than an allegation.Fundamental Analysis and Valuation / Quality and Distress
Sloan Accrual Measure
Reconcile changes in noncash working capital, short-term debt, taxes payable, and depreciation into one signed accrual measure.Fundamental Analysis and Valuation / Quality and Distress
Ohlson O-Score
Build Model 1, retain its nine variables and logistic transformation, and preserve the historical 3.8% screening cutoff without calling it a universal default probability.Fundamental Analysis and Valuation / Quality and Distress
Zmijewski X-Score
Calculate the X-index and normal-CDF mapping while keeping sampling-bias research and the zero-index screen explicit.Fundamental Analysis and Valuation / Quality and Distress
Springate S-Score
Build the 1978 Canadian four-factor convention and expose the 0.862 cutoff and primary-source availability limitation.Fundamental Analysis and Valuation / Quality and Distress
Taffler Z-Score
Calculate the four-factor transformed convention while making the no-credit-interval construction and coefficient-variant risk visible.Fundamental Analysis and Valuation / Quality and Distress
Fulmer H-Score
Reconcile all nine terms and expose the logarithmic unit-scale dependency that can otherwise make the score irreproducible.Fundamental Analysis and Valuation / Quality and Distress
Grover G-Score
Implement the reported equation while being explicit that the original primary model document was not located in an authoritative open repository.Fundamental Analysis and Valuation / Quality and Distress
Dechow F-Score for Misstatement Risk
Derive RSST accruals through actual issuance, expose the logit and unconditional-probability scaling, and keep the result separate from a fraud finding.Fundamental Analysis and Valuation / Quality and Distress
Dechow-Dichev Accrual Quality
Estimate the original firm-specific regression, inspect every residual, and enforce the retrospective availability boundary created by future CFO.Fundamental Analysis and Valuation / Quality and Distress
Modified Jones Discretionary Accrual Model
Fit the peer model, subtract receivables change from revenue change, and preserve sample construction and residual uncertainty.Fundamental Analysis and Valuation / Integrated Equity Scoring
Point-in-Time Stock-Scoring Input Assembly
Assemble a reproducible stock-scoring input record without allowing later restatements, future filings, or mixed units to leak into an earlier decision.Fundamental Analysis and Valuation / Integrated Equity Scoring
Stock-Scoring Peer Cohort Resolver
Resolve a reproducible peer set using sector, country, listing, market-cap, and availability rules before calculating cross-sectional diagnostics.Fundamental Analysis and Valuation / Integrated Equity Scoring
Fundamental Metric Direction and Peer Normalization
Normalize heterogeneous fundamentals with an explicit higher-is-better direction and a reproducible midrank percentile rather than an opaque vendor grade.Fundamental Analysis and Valuation / Integrated Equity Scoring
Model Applicability and Variant Router
Route model requests through explicit population, period, framework, and data requirements before any score is interpreted.Fundamental Analysis and Valuation / Integrated Equity Scoring
Accounting Financial-Health Composite
Build a bounded four-pillar financial-health score with frozen weights, component cards, and a reconciliation that survives review.Fundamental Analysis and Valuation / Integrated Equity Scoring
Earnings-Quality Composite
Create a bounded earnings-quality component that preserves each diagnostic's meaning, direction, and evidence boundary.Fundamental Analysis and Valuation / Integrated Equity Scoring
Dividend Safety Score
Build a dividend-safety score from free-cash-flow coverage, earnings coverage, interest coverage, and cash buffer with explicit caps and no-dividend routing.Fundamental Analysis and Valuation / Integrated Equity Scoring
Balance-Sheet Resilience Score
Build a bounded resilience score that exposes its four balance-sheet components and rejects economically invalid denominators.Fundamental Analysis and Valuation / Integrated Equity Scoring
Distress-Model Ensemble
Aggregate supplied model probabilities with explicit weights, dispersion, and disagreement diagnostics instead of hiding model conflict inside one number.Fundamental Analysis and Valuation / Integrated Equity Scoring
Cross-Model Conflict and Double-Counting Resolver
Resolve duplicate evidence groups with a transparent cap and flag within-group disagreement instead of allowing repeated signals to dominate.Fundamental Analysis and Valuation / Integrated Equity Scoring
Overall Explainable Stock Score
Combine six declared pillars into a single bounded score while retaining the exact contribution bridge and interpretation band.Fundamental Analysis and Valuation / Integrated Equity Scoring
Score Confidence, Missing-Data Penalty, and Abstention
Turn coverage, staleness, and conflict into an explicit confidence value, adjusted score, and abstention state.Fundamental Analysis and Valuation / Integrated Equity Scoring
Market-Wide Stock Screening and Ranking
Screen a dated synthetic universe with explicit inclusion gates and deterministic score/confidence/ID ranking.Fundamental Analysis and Valuation / Integrated Equity Scoring
Stock Score History, Migration, and Change Attribution
Compare strictly chronological score snapshots, identify band migration, and attribute the latest change to the largest component delta without hindsight.Fundamental Analysis and Valuation / Sector-Specific Equity Scoring
Bank Fundamental Score
Build an auditable bank review score whose prudential floors remain visible beside—not hidden inside—the composite.Fundamental Analysis and Valuation / Sector-Specific Equity Scoring
Insurance Fundamental Score
Construct a Solvency-II-tagged insurer score that keeps capital requirements and underwriting economics separately inspectable.Fundamental Analysis and Valuation / Sector-Specific Equity Scoring
REIT Fundamental Score
Build a transparent equity-REIT score that labels every non-GAAP bridge and never presents package AFFO as a standardized measure.Fundamental Analysis and Valuation / Sector-Specific Equity Scoring
Utility Fundamental Score
Create a regulated-utility score that connects accounting evidence to ratemaking economics without treating an allowed return as guaranteed earnings.Fundamental Analysis and Valuation / Sector-Specific Equity Scoring
Early-Stage Liquidity and Runway Score
Build a transparent runway sensitivity that preserves the monthly cash-flow path and labels nonburning, short-window, and negative-liquidity states.Fundamental Analysis and Valuation / Sector-Specific Equity Scoring
Cyclical and Commodity-Cycle Normalization
Build a reproducible mid-cycle sensitivity whose window, medians, current cycle position, and nonpositive-EBITDA state are fully exposed.Fundamental Analysis and Valuation / Sector-Specific Equity Scoring
Holding-Company Look-Through Score
Build a holding-company score around an attributable stake ledger and a visible parent bridge from gross asset value to NAV.Fundamental Analysis and Valuation / Sector-Specific Equity Scoring
Sector-Specific Weight Calibration
Calibrate a candidate weight vector with a frozen temporal split, compare Brier losses, and retain the base vector whenever holdout performance does not improve.Fundamental Analysis and Valuation / Sector-Specific Equity Scoring
Unsupported-Scope and Coverage Decision
Create a deterministic coverage gate that checks sector support, framework identity, required fields, knowledge dates, and staleness before selecting a stable model ID.Credit Risk and Default / Probability of Default
Logistic PD Model
Turn a versioned linear credit score into an auditable probability, odds, contribution trace, and threshold state without pretending that scoring is calibration.Credit Risk and Default / Probability of Default
Probit PD Model
Build an auditable probit inference path and compare its link geometry with logistic scoring without treating the two coefficient scales as interchangeable.Credit Risk and Default / Probability of Default
Through-the-Cycle PD
Calculate a transparent long-run average one-year PD, retain the annual rates and pooled-rate comparison, and expose the representativeness assumptions behind through-the-cycle calibration.Credit Risk and Default / Probability of Default
Point-in-Time PD
Build a log-odds PIT bridge that exposes borrower and macro shifts separately while making clear that IFRS 9 and regulatory implementations require much more than this teaching formula.Credit Risk and Default / Probability of Default
Merton Distance-to-Default
Solve the coupled equity equations, separate physical and risk-neutral measures, and expose convergence, drift, default-point, and model-assumption risk.Credit Risk and Default / Probability of Default
Campbell-Hilscher-Szilagyi Distress Probability
Reproduce the published score contribution by contribution while preserving the paper's variable definitions, lag, failure label, sample boundary, and recalibration warning.Credit Risk and Default / Probability of Default
Bharath-Shumway Naive Distance-to-Default
Calculate naïve firm value, debt volatility, asset volatility, distance, and normal-CDF probability while preserving every approximation and empirical-use boundary.Digital Assets and On-Chain Finance / AMM Pricing
Constant-Product AMM
The x · y = k curve behind Uniswap v2. Price is set by the reserve ratio, so every trade moves it — and the slippage a trade suffers is a deterministic function of its size relative to the pool.Digital Assets and On-Chain Finance / AMM Pricing
Constant-Sum AMM
The x + y = k curve: zero slippage, and the pool can be fully drained of one asset.Digital Assets and On-Chain Finance / AMM Pricing
StableSwap Invariant
Curve's invariant: nearly constant-sum near the peg, constant-product away from it.Digital Assets and On-Chain Finance / AMM Pricing
Weighted-Product AMM
Balancer's generalisation of constant product to arbitrary weights, so a pool can hold 80/20 rather than 50/50.Digital Assets and On-Chain Finance / AMM Pricing
Concentrated-Liquidity Position
Uniswap v3 positions: liquidity supplied only within a price range.Digital Assets and On-Chain Finance / Liquidity and Liquidation
Impermanent-Loss Calculation
Value lost by providing liquidity rather than simply holding the two assets.Digital Assets and On-Chain Finance / Liquidity and Liquidation
Liquidity-Provider Fee APR
Simple non-compounded LP fee APR from a daily volume-and-fee ledger divided by time-weighted capital.Digital Assets and On-Chain Finance / Liquidity and Liquidation
Collateral-Health Factor
The ratio of weighted collateral to debt in a lending position.Digital Assets and On-Chain Finance / Liquidity and Liquidation
Liquidation-Price Calculation
The collateral price at which a position becomes liquidatable.Digital Assets and On-Chain Finance / Liquidity and Liquidation
Liquidation Waterfall
The order in which collateral is seized and debt repaid, including liquidation bonus and any protocol fee.Model Validation and Backtesting / Classification and Score Validation
ROC Curve and ROC-AUC
Build a tie-aware ROC ledger that exposes every threshold, weighted confusion count, curve point, and pairwise-ranking area.Model Validation and Backtesting / Classification and Score Validation
Precision-Recall Curve and PR-AUC
Build a prevalence-aware precision-recall ledger and calculate average precision without silently substituting trapezoidal PR area.Model Validation and Backtesting / Classification and Score Validation
Brier Score
Calculate a weighted Brier score with an auditable climatology baseline and no confusion between probability error and calibration alone.Model Validation and Backtesting / Classification and Score Validation
Log Loss
Calculate binary log loss while making probability clipping, overconfidence, and weight semantics visible.Model Validation and Backtesting / Classification and Score Validation
Reliability Diagram and Expected Calibration Error
Build a complete reliability table and equal-width ECE while preserving empty bins, support, and bin-sensitivity limitations.Model Validation and Backtesting / Classification and Score Validation
Gains, Lift, and Decile Capture
Build a deterministic gains-and-lift table that exposes bucket assignment, ties, cumulative capture, and the random baseline.Model Validation and Backtesting / Classification and Score Validation
Cost-Sensitive Threshold Optimization
Enumerate and audit every candidate threshold, confusion matrix, selected rate, and expected cost instead of hiding a policy inside one number.Model Validation and Backtesting / Classification and Score Validation
Score Stability and Migration Matrix
Build a matched-entity stability and migration ledger with fixed bands, directional movement, and distribution change kept distinct.Model Validation and Backtesting / Classification and Score Validation
Slice-Based Validation by Sector, Country, and Regime
Build a support-aware slice ledger that reports Brier, log loss, ROC-AUC, prevalence, and explicit low-support or single-class states.Model Validation and Backtesting / Classification and Score Validation
Rare-Event Backtest and Confidence Bounds
Backtest a rare binary event with a point estimate, expected count, finite Wilson interval, and explicit sampling assumptions.Earnings and Per-Share Analytics / Earnings and Share Foundations
Stock-Split/Consolidation EPS Restatement
Restate Basic EPS after stock splits and share consolidations with exact factors, basis-aware event selection, reporting cutoffs, and reproducible controls.Earnings and Per-Share Analytics / Earnings and Share Foundations
Bonus-Issue EPS Restatement
Derive and apply the exact EPS restatement factor for bonus and capitalisation issues without confusing bonus shares added with total post-issue shares.Earnings and Per-Share Analytics / Earnings and Share Foundations
Rights-Issue Bonus-Factor Adjustment
Calculate TERP and the exact rights-issue bonus factor without retrospectively treating cash-funded shares as free.Earnings and Per-Share Analytics / Earnings and Share Foundations
Basic EPS
Basic earnings per share: profit attributable to ordinary shareholders over the weighted average shares outstanding.Earnings and Per-Share Analytics / Basic and Diluted EPS
If-Converted Convertible-Debt Dilution
Build the after-tax numerator adjustment, weighted conversion shares, and exact antidilution test for convertible-debt diluted EPS.Earnings and Per-Share Analytics / Basic and Diluted EPS
If-Converted Convertible-Preference Dilution
Build the exact if-converted EPS candidate, handle timing correctly, and know when apparent dilution must be excluded.Earnings and Per-Share Analytics / Basic and Diluted EPS
Treasury-Share Method for Options/Warrants
Build an exact diluted-EPS denominator bridge without blending US-GAAP and IAS 33 proceeds rules.Earnings and Per-Share Analytics / Basic and Diluted EPS