# Statistical Time Series — fintech-algorithms > 29 algorithms in 5 families, sliced out of the > fintech-algorithms reference. Zero-dependency TypeScript: plain arrays and objects in, > plain values out. This file covers D09 only. D09 · 29 topics · 5 families · 12 verified Install: npm install fintech-algorithms Agent skill (install it rather than re-deriving this file): npx skills add IslamBaraka90/Fintech-Algorithms-Library what it is: https://docs.thefintechbuilder.com/guides/agent-skill/ Source: fintech-algorithms@0.12.0 · payload schema 2.0.0 Reference payload: https://docs.thefintechbuilder.com/reference/payload.json Version endpoint: https://docs.thefintechbuilder.com/version.json Domain page: https://docs.thefintechbuilder.com/statistical-time-series/ Full index (324 topics across 13 domains): https://docs.thefintechbuilder.com/llms.txt Verification tiers: - verified — the worked example is the figure published in the algorithm's article, replayed and asserted by the test suite on every run. The arithmetic cannot drift without the build failing. Treat the numbers as reproducible. - contract — the module loads, the entry point is callable and its declared signature matches the compiled code. The example is real captured output, but no independently published figure asserts it. Treat the shape as reliable and the numbers as unattested. Full explanation: https://docs.thefintechbuilder.com/guides/verification/ Each entry: name — signature — archetype — verification tier — docs URL From the docs URL, mechanically: import subpath — swap the https://docs.thefintechbuilder.com/ prefix for fintech-algorithms/ and drop the trailing slash markdown page — append index.md; same contract as the HTML page, a fraction of the bytes ## D09-F01 — Diagnostics https://docs.thefintechbuilder.com/statistical-time-series/diagnostics/ - ACF — `acf(values, maxLag)` — record-transform — contract — https://docs.thefintechbuilder.com/statistical-time-series/diagnostics/acf/ - PACF — `pacf(values, maxLag)` — record-transform — contract — https://docs.thefintechbuilder.com/statistical-time-series/diagnostics/pacf/ - Augmented Dickey-Fuller — `adf(values, lags, criticalValue)` — record-transform — contract — https://docs.thefintechbuilder.com/statistical-time-series/diagnostics/augmented-dickey-fuller/ - KPSS — `kpss(values, lags, criticalValue)` — record-transform — contract — https://docs.thefintechbuilder.com/statistical-time-series/diagnostics/kpss/ - Ljung-Box — `ljungBox(values, lags, modelDf, alpha)` — record-transform — contract — https://docs.thefintechbuilder.com/statistical-time-series/diagnostics/ljung-box/ - Zivot-Andrews Break Test — `zivotAndrews(values, lags, trim, criticalValue)` — record-transform — contract — https://docs.thefintechbuilder.com/statistical-time-series/diagnostics/zivot-andrews-break-test/ ## D09-F02 — Forecast Models https://docs.thefintechbuilder.com/statistical-time-series/forecast-models/ - AutoReg — `forecastAutoReg(values, ar, intercept, horizon)` — record-transform — verified — https://docs.thefintechbuilder.com/statistical-time-series/forecast-models/autoreg/ - ARMA — `forecastARMA(values, ar, ma, intercept, horizon)` — record-transform — verified — https://docs.thefintechbuilder.com/statistical-time-series/forecast-models/arma/ - ARIMA — `forecastARIMA(values, ar, ma, intercept, differenceOrder, horizon)` — record-transform — verified — https://docs.thefintechbuilder.com/statistical-time-series/forecast-models/arima/ - SARIMA/SARIMAX — `forecastSARIMAX(values, exog, futureExog, beta, ar, ma, seasonalAr, seasonalMa, intercept, differenceOrder, seasonalDifferenceOrder, period, horizon)` — record-transform — verified — https://docs.thefintechbuilder.com/statistical-time-series/forecast-models/sarima-sarimax/ - Holt-Winters — `forecastHoltWintersAdditive(values, alpha, beta, gamma, period, horizon, initialLevel, initialTrend, initialSeasonals)` — record-transform — verified — https://docs.thefintechbuilder.com/statistical-time-series/forecast-models/holt-winters/ - Theta Forecast — `forecastTheta(values, alpha, horizon)` — record-transform — verified — https://docs.thefintechbuilder.com/statistical-time-series/forecast-models/theta-forecast/ ## D09-F03 — Multivariate Systems https://docs.thefintechbuilder.com/statistical-time-series/multivariate-systems/ - VAR — `fitVAR(values, lags, includeIntercept)` — record-transform — contract — https://docs.thefintechbuilder.com/statistical-time-series/multivariate-systems/var/ - Structural VAR — `fitRecursiveSVAR(values, lags)` — record-transform — contract — https://docs.thefintechbuilder.com/statistical-time-series/multivariate-systems/structural-var/ - VECM — `fitVECMFixedBeta(values, beta, differenceLags, includeIntercept)` — record-transform — contract — https://docs.thefintechbuilder.com/statistical-time-series/multivariate-systems/vecm/ - Impulse-Response Analysis — `impulseResponses(coefficients, horizon)` — record-transform — contract — https://docs.thefintechbuilder.com/statistical-time-series/multivariate-systems/impulse-response-analysis/ - Forecast-Error Variance Decomposition — `forecastErrorVarianceDecomposition(coefficients, sigmaU, horizon)` — record-transform — contract — https://docs.thefintechbuilder.com/statistical-time-series/multivariate-systems/forecast-error-variance-decomposition/ ## D09-F04 — State and Regime Models https://docs.thefintechbuilder.com/statistical-time-series/state-and-regime-models/ - Kalman Filter — `runFilter(observations, config)` — record-transform — verified — https://docs.thefintechbuilder.com/statistical-time-series/state-and-regime-models/kalman-filter/ - Extended Kalman Filter — `runFilter(observations, config)` — record-transform — verified — https://docs.thefintechbuilder.com/statistical-time-series/state-and-regime-models/extended-kalman-filter/ - Unscented Kalman Filter — `runFilter(observations, config)` — record-transform — verified — https://docs.thefintechbuilder.com/statistical-time-series/state-and-regime-models/unscented-kalman-filter/ - Hidden Markov Model — `runFilter(observations, config)` — record-transform — verified — https://docs.thefintechbuilder.com/statistical-time-series/state-and-regime-models/hidden-markov-model/ - Markov-Switching Autoregression — `runFilter(observations, config)` — record-transform — verified — https://docs.thefintechbuilder.com/statistical-time-series/state-and-regime-models/markov-switching-autoregression/ - Bayesian Change-Point Detection — `runFilter(observations, config)` — record-transform — verified — https://docs.thefintechbuilder.com/statistical-time-series/state-and-regime-models/bayesian-change-point-detection/ ## D09-F05 — Decomposition and Cycles https://docs.thefintechbuilder.com/statistical-time-series/decomposition-and-cycles/ - STL Decomposition — `stlDecompose(values, period, seasonalWindow, trendWindow, robustIterations)` — record-transform — contract — https://docs.thefintechbuilder.com/statistical-time-series/decomposition-and-cycles/stl-decomposition/ - Hodrick-Prescott Filter — `hpFilter(values, smoothing)` — record-transform — contract — https://docs.thefintechbuilder.com/statistical-time-series/decomposition-and-cycles/hodrick-prescott-filter/ - Baxter-King Filter — `bkFilter(values, low, high, K)` — record-transform — contract — https://docs.thefintechbuilder.com/statistical-time-series/decomposition-and-cycles/baxter-king-filter/ - Christiano-Fitzgerald Filter — `cfFilter(values, low, high, drift)` — record-transform — contract — https://docs.thefintechbuilder.com/statistical-time-series/decomposition-and-cycles/christiano-fitzgerald-filter/ - Fast Fourier Transform Periodogram — `fftPeriodogram(values, sampleFrequency, detrend, window)` — record-transform — contract — https://docs.thefintechbuilder.com/statistical-time-series/decomposition-and-cycles/fast-fourier-transform-periodogram/ - Wavelet Decomposition — `haarWavelet(values, levels)` — record-transform — contract — https://docs.thefintechbuilder.com/statistical-time-series/decomposition-and-cycles/wavelet-decomposition/