stationaritet

Stationarity, or stationaritet in Norwegian usage, describes a property of a stochastic process in which its statistical characteristics do not change over time. In time series analysis, stationarity is a central assumption for many methods and inferences.

Two main notions exist: strict (full) stationarity and weak (second-order) stationarity. A process is strictly stationary if the joint distribution of any set of observations is unchanged by a time shift. Weak stationarity requires a constant mean and autocovariance that depends only on lag, not on time.

Non-stationary processes may exhibit trends, seasonality, changing variance, or unit roots. They complicate estimation and forecasting since moments can evolve over time. Common remedies include differencing (as in ARIMA), detrending, or applying transformations such as logarithms to stabilize variance.

Tests and practice: Stationarity is commonly assessed with unit-root tests like the Augmented Dickey-Fuller test and with tests for level or trend stationarity such as KPSS. If a series is non-stationary but has a stable long-run relationship with another series, cointegration may be modeled.

Examples: White noise is both strictly and weakly stationary. A random walk with drift is non-stationary, though its first difference is a white-noise process. ARMA models assume weak stationarity; differencing is used to induce stationarity before modeling.