Domain atlas/D07/Technical Indicators

D07 / Territory 7 of 49

Technical Indicators

Describe trend, momentum, volatility, volume, and cycles.

137 released builds 9 algorithm familiesIn release

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Every card below is included in the current governed release with its article, sources, Python, TypeScript, and available labs.

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D07-F01

Trend Smoothing

24 builds

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.

12 min Python + TypeScriptFoundation

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.

11 min Python + TypeScriptIntermediate

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.

10 min Python + TypeScriptFoundation

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.

9 min Python + TypeScriptIntermediate

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.

9 min Python + TypeScriptIntermediate

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)).

6 min Python + TypeScriptIntermediate

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).

8 min Python + TypeScriptIntermediate

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.

11 min Python + TypeScriptAdvanced

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.

8 min Python + TypeScriptAdvanced

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.

13 min Python + TypeScriptIntermediate

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.

13 min Python + TypeScriptIntermediate

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.

13 min Python + TypeScriptIntermediate

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.

13 min Python + TypeScriptIntermediate

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.

13 min Python + TypeScriptIntermediate

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.

13 min Python + TypeScriptIntermediate

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.

13 min Python + TypeScriptIntermediate

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.

13 min Python + TypeScriptIntermediate

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.

13 min Python + TypeScriptIntermediate

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…

13 min Python + TypeScriptIntermediate

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.

13 min Python + TypeScriptIntermediate

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.

13 min Python + TypeScriptIntermediate

Technical Indicators / Trend Smoothing

Gaussian Moving Average

Averages close under a Gaussian weight curve centred at offset * (period - 1) with width period / sigma.

13 min Python + TypeScriptIntermediate

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.

13 min Python + TypeScriptIntermediate

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.

13 min Python + TypeScriptIntermediate

D07-F02

Trend Systems

19 builds

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.

15 min Python + TypeScriptIntermediate

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.

7 min Python + TypeScriptIntermediate

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.

7 min Python + TypeScriptIntermediate

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.

7 min Python + TypeScriptAdvanced

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.

6 min Python + TypeScriptAdvanced

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.

7 min Python + TypeScriptAdvanced

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.

7 min Python + TypeScriptAdvanced

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.

7 min Python + TypeScriptAdvanced

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.

13 min Python + TypeScriptIntermediate

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.

13 min Python + TypeScriptIntermediate

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.

13 min Python + TypeScriptIntermediate

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.

13 min Python + TypeScriptIntermediate

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.

12 min Python + TypeScriptIntermediate

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.

13 min Python + TypeScriptIntermediate

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.

13 min Python + TypeScriptIntermediate

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.

13 min Python + TypeScriptIntermediate

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.

13 min Python + TypeScriptIntermediate

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.

13 min Python + TypeScriptIntermediate

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.

13 min Python + TypeScriptIntermediate

D07-F03