Time Series Statistical Tests

`ts-stat-tests`

Motivation

Time Series Analysis has been around for a long time, especially for doing Statistical Testing. Some Python packages are going a long way to make this even easier than it has ever been before. Such as sktime and pycaret and pmdarima and statsmodels.

There are some typical Statistical Tests which are accessible in these Python (QS, Normality, Stability, etc). However, there are still some statistical tests which are not yet ported over to Python, but which have been written in R and are quite stable.

Moreover, there is no one single library package for doing time-series statistical tests in Python.

That’s exactly what this package aims to achieve.

A single package for doing all the standard time-series statistical tests.

Tests

Full credit goes to the packages listed in this table.

Type	Name	Source Package	Source Language	Implemented
Correlation	Auto-Correlation function (ACF)	`statsmodels`	Python	✅
Correlation	Partial Auto-Correlation function (PACF)	`statsmodels`	Python	✅
Correlation	Cross-Correlation function (CCF)	`statsmodels`	Python	✅
Correlation	Ljung-Box test of autocorrelation in residuals (LB)	`statsmodels`	Python	✅
Correlation	Lagrange Multiplier tests for autocorrelation (LM)	`statsmodels`	Python	✅
Correlation	Breusch-Godfrey Lagrange Multiplier tests for residual autocorrelation (BGLM)	`statsmodels`	Python	✅
Regularity	Approximate Entropy	`antropy`	python	✅
Regularity	Sample Entropy	`antropy`	python	✅
Regularity	Permutation Entropy	`antropy`	python	✅
Regularity	Spectral Entropy	`antropy`	python	✅
Seasonality	QS	`seastests`	R	✅
Seasonality	Osborn-Chui-Smith-Birchenhall test of seasonality (OCSB)	`pmdarima`	Python	✅
Seasonality	Canova-Hansen test for seasonal differences (CH)	`pmdarima`	Python	✅
Seasonality	Seasonal Strength	`tsfeatures`	Python	✅
Seasonality	Trend Strength	`tsfeatures`	Python	✅
Seasonality	Spikiness	`tsfeatures`	Python	✅
Stability	Stability	`tsfeatures`	Python	✅
Stability	Lumpiness	`tsfeatures`	Python	✅
Stationarity	Augmented Dickey-Fuller test for stationarity (ADF)	`statsmodels`	Python	✅
Stationarity	Kwiatkowski-Phillips-Schmidt-Shin test for stationarity (KPSS)	`statsmodels`	Python	✅
Stationarity	Range unit-root test for stationarity (RUR)	`statsmodels`	Python	✅
Stationarity	Zivot-Andrews structural-break unit-root test (ZA)	`statsmodels`	Python	✅
Stationarity	Phillips-Peron test for stationarity (PP)	`pmdarima`	Python	✅
Stationarity	Elliott-Rothenberg-Stock (ERS) de-trended Dickey-Fuller test	`arch`	Python	✅
Stationarity	Variance Ratio (VR) test for a random walk	`arch`	Python	✅
Normality	Jarque-Bera test of normality (JB)	`statsmodels`	Python	🔲
Normality	Omnibus test for normality (OB)	`statsmodels`	Python	🔲
Normality	Shapiro-Wilk test for normality (SW)	`scipy`	Python	🔲
Normality	D’Agostino & Pearson’s test for normality	`scipy`	Python	🔲
Normality	Anderson-Darling test for normality	`scipy`	Python	🔲
Linearity	Harvey Collier test for linearity (HC)	`statsmodels`	Python	🔲
Linearity	Lagrange Multiplier test for linearity (LM)	`statsmodels`	Python	🔲
Linearity	Rainbow test for linearity (RB)	`statsmodels`	Python	🔲
Linearity	Ramsey’s RESET test for neglected nonlinearity (RR)	`statsmodels`	Python	🔲
Heteroscedasticity	Engle’s Test for Autoregressive Conditional Heteroscedasticity (ARCH)	`statsmodels`	Python	🔲
Heteroscedasticity	Breusch-Pagan Lagrange Multiplier test for heteroscedasticity (BPL)	`statsmodels`	Python	🔲
Heteroscedasticity	Goldfeld-Quandt test for homoskedasticity (GQ)	`statsmodels`	Python	🔲
Heteroscedasticity	White’s Lagrange Multiplier Test for Heteroscedasticity (WLM)	`statsmodels`	Python	🔲

Known limitations

These listed tests is not exhaustive, and there is probably some more that could be added. Therefore, we encourage you to raise issues or pull requests to add more statistical tests to this suite.
This package does not re-invent any of these tests. It merely calls the underlying packages, and calls the functions which are already written elsewhere.