> ## Documentation Index
> Fetch the complete documentation index at: https://docs.fincept.in/llms.txt
> Use this file to discover all available pages before exploring further.

# Time-series analysis

> Autocorrelation, partial autocorrelation and cross-correlation with Ljung-Box tests; unit-root and stationarity tests (ADF, KPSS, Zivot-Andrews, range); Engle-Granger cointegration; BDS independence and variance-break tests; classical, STL and MSTL seasonal decomposition; Hodrick-Prescott, Baxter-King and Christiano-Fitzgerald filters, polynomial detrending and the periodogram.

Toolset `stats_tsa_analysis`: 9 tools.

| Tool | What it does | Notes |
| - | - | - |
| `stats_correlogram` | Autocorrelation (ACF) and partial autocorrelation (PACF) of one series up to nlags, each with its confidence band, plus the autocovariances and the Ljung-Box and Box-Pierce Q statistics with p-values at every lag. | |
| `stats_cross_correlogram` | Cross-correlation of two equally long series at lags −nlags to +nlags: the value at lag k is corr(x\[t+k], y\[t]), so a peak at k > 0 means y leads x by k periods and at k \< 0 that x leads y. | |
| `stats_seasonal_decompose` | Splits a series into trend, seasonal and residual components by STL (LOESS, default), classical moving averages (additive or multiplicative) or MSTL (several seasonal periods at once). | |
| `stats_trend_cycle_filter` | Separates a series into trend and cycle with the Hodrick-Prescott filter, the Baxter-King or Christiano-Fitzgerald band-pass filters (cycles between low and high periods), or a polynomial detrend. | |
| `stats_periodogram` | Spectral density of a series by the periodogram or Welch's averaged periodogram. | |
| `stats_stationarity_test` | Unit-root and stationarity tests on one series: augmented Dickey-Fuller (null: unit root), KPSS (null: stationary), both together with a joint verdict (default), Zivot-Andrews (unit root against stationarity with one structural break, whose date it reports) and the range unit-root test. | core |
| `stats_engle_granger` | Engle-Granger two-step cointegration test of y on one to five x columns: an ADF test on the residual of the cointegrating regression with MacKinnon p-values (null: no cointegration). | |
| `stats_bds_test` | BDS test of the null that a series is independent and identically distributed, at embedding dimensions 2 to max\_dim. | |
| `stats_breakvar_test` | Test of a change in variance between the first and last parts of a series (usually model residuals): the ratio of the sums of squares of the last and first subsets. | |

Inputs, limits and outputs are described in [Fincept Stats](/guides/fincept-stats). Full schemas: `fincept_describe_tool`.


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