Nichtstationaritäten

Nichtstationaritäten, often translated as non-stationarities, refer to a condition in time series data where the statistical properties of the series change over time. These properties typically include the mean, variance, and autocorrelation structure. A stationary time series, in contrast, has statistical properties that are constant over time. The presence of non-stationarities can pose significant challenges for statistical modeling and forecasting, as many standard time series models assume stationarity.

Common types of non-stationarities include trends, where the mean of the series systematically increases or decreases over time, and structural breaks, which are abrupt changes in the statistical properties of the series. Seasonality can also be considered a form of non-stationarity if its amplitude or phase shifts over time.

Detecting non-stationarities is a crucial first step in time series analysis. Various statistical tests, such as the Augmented Dickey-Fuller test or the Kwiatkowski-Phillips-Schmidt-Shin test, are used to identify the presence of unit roots, a common indicator of non-stationarity.

To address non-stationarities, several techniques can be employed. Differencing is a common method where the difference between consecutive observations is taken to remove trends and stabilize the variance. Transformations, such as logarithmic transformations, can also help in stabilizing variance. Models like ARIMA (Autoregressive Integrated Moving Average) explicitly incorporate differencing to handle non-stationary data. More advanced techniques include the use of cointegration analysis for series that are non-stationary individually but have a long-run linear relationship, or state-space models that can explicitly model time-varying parameters.