ickestationärt

Ickestationärt is a term that appears in some German-language writings to denote non-stationarity in time series analysis. It is not part of standard statistical terminology; the widely accepted form is nichtstationär. The concept describes processes whose probabilistic properties change over time rather than remaining constant across observations.

A time series is non-stationary when aspects such as its mean, variance, or autocovariance depend on time. Weak or second-order non-stationarity allows the mean or variance to vary over time, while strict or strong non-stationarity means the entire distribution changes with time. Common causes include deterministic trends, stochastic trends (unit roots), or time-varying volatility (heteroskedasticity).

Typical examples include a random walk with drift, which has a mean that drifts over time; a series with a persistent trend; and processes whose variance grows or shrinks over time. Non-stationarity complicates statistical inference because many models assume constant moments and stable relationships over time.

Testing and handling non-stationarity are central tasks in time series analysis. Tests such as the Augmented Dickey-Fuller (ADF) test and the Phillips-Perron test assess the presence of unit roots, while the KPSS test evaluates stationarity around a deterministic trend. When non-stationarity is present, differencing the series, detrending, or applying a transformation (for example, logarithmic or Box-Cox) can induce stationarity. For relationships among multiple non-stationary series, cointegration may allow for stable long-run equilibria, enabling modeling with error-correction or cointegrated VAR models. Other approaches include fractionally integrated models or state-space formulations that accommodate evolving dynamics.