Ickestationaritetens

Ickestationaritetens is the Swedish term for non-stationarity, a property of a stochastic process in which its statistical characteristics change over time. In a stationary process, moments such as the mean and variance are constant and the dependence structure depends only on the time gap between observations. Non-stationarity occurs when the mean, variance, or autocovariance evolve with time, complicating analysis and forecasting.

Two broad notions are commonly used: weak (second-order) non-stationarity, where the mean and autocovariances depend on time, and strong (strict) non-stationarity, where the entire distribution changes over time. In practice, weak non-stationarity is the central concern for time series modeling.

Causes include deterministic trends, stochastic trends such as unit roots (random walks), structural breaks, regime shifts, and changing volatility (heteroskedasticity).

Detection and handling: unit-root tests like the Augmented Dickey-Fuller and Phillips-Perron tests help identify non-stationarity due to a unit root; the KPSS test assesses stationarity. Common remedies include differencing the series to obtain an I(d) process, detrending to remove deterministic trends, or applying transformations. For multivariate series, cointegration can produce stationary relations between non-stationary components. Modeling strategies include ARIMA for univariate series and cointegrated VAR for multiple series; volatility models like GARCH address changing variance.

Why it matters: non-stationarity can invalidate standard statistical methods that assume constant moments and stable relationships, making reliable inference and forecasting more challenging. Many real-world phenomena, including economic indicators and climate variables, exhibit some form of ickestationaritetens.