Stationaritätsbedingungen

Stationaritätsbedingungen, often translated as stationarity conditions, are fundamental concepts in time series analysis. A time series is considered stationary if its statistical properties, such as its mean, variance, and autocorrelation, do not change over time. This means the behavior of the series remains consistent throughout its observed period.

There are two main types of stationarity: strict stationarity and weak (or covariance) stationarity. Strict stationarity implies that the joint probability distribution of any set of observations remains invariant under shifts in time. This is a very strong condition and rarely met in practice. Weak stationarity is a more practical and commonly used concept. For a time series to be weakly stationary, its mean must be constant over time, its variance must be constant over time, and the autocovariance between two time points must depend only on the time lag between them, not on their absolute position in time.

Stationarity is a crucial assumption for many statistical modeling techniques applied to time series data, including autoregressive (AR), moving average (MA), and ARIMA models. If a time series is not stationary, it often needs to be transformed, for example, by differencing, to achieve stationarity before these models can be reliably applied. Non-stationarity can lead to spurious regressions and unreliable forecasts. Therefore, checking for stationarity is a standard initial step in any time series analysis.