D09 / Territory 9 of 49
Statistical Time Series
Model temporal dependence and forecast distributions.
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in this territory.
Every card below is included in the current governed release with its article, sources, Python, TypeScript, and available labs.
Search the released libraryDiagnostics
6 buildsStatistical 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.Forecast Models
6 buildsStatistical 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.Multivariate Systems
5 buildsStatistical 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.State and Regime Models
6 buildsStatistical 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.Decomposition and Cycles
6 buildsStatistical 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.Hilbert and Ehlers Cycle Analytics
8 buildsStatistical 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.Territory coverage
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