Statistical Time Series

37 algorithms · 6 families · D09

Reading this with a program? statistical-time-series/llms.txt lists all 37 algorithms here — signature, shape and verification tier, one line each. Every reference page below also exists as markdown at <page URL>index.md.

Diagnostics #

ACF contract acf(values, maxLag)
PACF contract pacf(values, maxLag)
Augmented Dickey-Fuller contract adf(values, lags, criticalValue)
KPSS contract kpss(values, lags, criticalValue)
Ljung-Box contract ljungBox(values, lags, modelDf, alpha)
Zivot-Andrews Break Test contract zivotAndrews(values, lags, trim, criticalValue)

Forecast Models #

AutoReg verified forecastAutoReg(values, ar, intercept, horizon)
ARMA verified forecastARMA(values, ar, ma, intercept, horizon)
ARIMA verified forecastARIMA(values, ar, ma, intercept, differenceOrder, horizon)
SARIMA/SARIMAX verified forecastSARIMAX(values, exog, futureExog, beta, ar, ma, seasonalAr, seasonalMa, intercept, differenceOrder, seasonalDifferenceOrder, period, horizon)
Holt-Winters verified forecastHoltWintersAdditive(values, alpha, beta, gamma, period, horizon, initialLevel, initialTrend, initialSeasonals)
Theta Forecast verified forecastTheta(values, alpha, horizon)

Multivariate Systems #

VAR contract fitVAR(values, lags, includeIntercept)
Structural VAR contract fitRecursiveSVAR(values, lags)
VECM contract fitVECMFixedBeta(values, beta, differenceLags, includeIntercept)
Impulse-Response Analysis contract impulseResponses(coefficients, horizon, impactMatrix)
Forecast-Error Variance Decomposition contract forecastErrorVarianceDecomposition(coefficients, sigmaU, horizon, impactMatrix)

State and Regime Models #

Kalman Filter verified runFilter(observations, config)
Extended Kalman Filter verified runFilter(observations, config)
Unscented Kalman Filter verified runFilter(observations, config)
Hidden Markov Model verified runFilter(observations, config)
Markov-Switching Autoregression verified runFilter(observations, config)
Bayesian Change-Point Detection verified runFilter(observations, config)

Decomposition and Cycles #

STL Decomposition contract stlDecompose(values, period, seasonalWindow, trendWindow, robustIterations)
Hodrick-Prescott Filter contract hpFilter(values, smoothing)
Baxter-King Filter contract bkFilter(values, low, high, K)
Christiano-Fitzgerald Filter contract cfFilter(values, low, high, drift)
Fast Fourier Transform Periodogram contract fftPeriodogram(values, sampleFrequency, detrend, window)
Wavelet Decomposition contract haarWavelet(values, levels)

Hilbert and Ehlers Cycle Analytics #

Hilbert Transform Dominant Cycle Period verified hilbertTransformDominantCyclePeriod(input)
Hilbert Transform Dominant Cycle Phase verified hilbertTransformDominantCyclePhase(input)
Hilbert Transform Phasor Components verified hilbertTransformPhasorComponents(input)
Hilbert Transform SineWave verified hilbertTransformSinewave(input)
Hilbert Transform Trend/Cycle Mode verified hilbertTransformTrendCycleMode(input)
Ehlers Cyber Cycle verified ehlersCyberCycle(input)
Ehlers Roofing Filter verified ehlersRoofingFilter(input)
Ehlers Decycler verified ehlersDecycler(input)

Statistical Time Series

Diagnostics#

Forecast Models#

Multivariate Systems#

State and Regime Models#

Decomposition and Cycles#