NichtStationaritätstests

NichtStationaritätstests, also known as tests for non-stationarity, are statistical tools used to determine whether a time series exhibits non-stationary behavior. A stationary time series has statistical properties, such as mean, variance, and autocorrelation, that do not change over time. Non-stationary time series, on the other hand, exhibit these properties changing over time.

The most common type of non-stationarity is a unit root process, which implies that shocks to the series have a permanent effect. The Augmented Dickey-Fuller (ADF) test is a widely used statistical test to detect the presence of a unit root in a time series. The null hypothesis of the ADF test is that the time series is non-stationary (has a unit root), while the alternative hypothesis is that it is stationary.

Another popular test is the Phillips-Perron (PP) test, which also tests for the presence of a unit root but is more robust to heteroskedasticity and autocorrelation in the error terms than the ADF test. The KPSS (Kwiatkowski-Phillips-Schmidt-Shin) test offers a different perspective. Its null hypothesis is that the time series is stationary, and the alternative hypothesis is that it is non-stationary. This inversion of hypotheses makes it a useful complement to the ADF and PP tests.

Identifying non-stationarity is crucial in time series analysis. Many standard econometric models assume stationarity. If a time series is non-stationary, it often needs to be transformed, for example, by differencing, to achieve stationarity before applying these models. Failure to account for non-stationarity can lead to spurious regression results and incorrect inferences.