Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test is used to analyze time series. The null hypothesis is that the time series is stationary. It is often used to complement an Augmented Dickey Fuller (ADF) test.

Two statistical tests would be used to check the stationarity of a time series – the Augmented Dickey Fuller (ADF) test and the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test. Both tests should be used. The ADF test null and alternate hypothesis are:

Null Hypothesis: The series has a unit root.

Alternate Hypothesis: The series has no unit root.

If the null hypothesis in failed to be rejected, this test may provide evidence that the series is non-stationary.

For the KPSS test the null and alternative hypotheses are reversed:

Null Hypothesis: The process is trend stationary.

Alternate Hypothesis: The series has a unit root (series is not stationary).