Unit root and stationarity tests

Unit root and stationarity tests allow to check if statistical properties of a time series do not vary with time. Available in Excel with the XLSTAT software.

What is stationarity?

A time series Yt (t=1,2...) is said to be stationary (in the week sense) if its statistical properties do not vary with time (expectation, variance, autocorrelation). The white noise is an example of a stationary time series, with for example the case where Yt follows a normal distribution N(µ, s²) independent of t.

Identifying that a series is not stationary allows to afterwards study where the non-stationarity comes from. A non-stationary series can, for example, be stationary in difference: Yt is not stationary, but the Yt - Yt-1 difference is stationary. It is the case of the random walk. A series can also be stationary in trend.

What are unit root and stationarity tests?

Stationarity tests allow verifying whether a series is stationary or not. There are two different approaches: some tests consider as null hypothesis H0 that the series is stationary (KPSS test, Leybourne and McCabe test), and for other tests, on the opposite, the null hypothesis is on the contrary that the series is not stationary (Dickey-Fuller test, augmented Dickey-Fuller test, Phillips-Perron test, DF-GLS test).

XLSTAT includes as of today includes all the above mentioned tests.