Nemstacionaritást

Nemstacionaritást (non-stationarity) is a property of a time series in which its statistical characteristics—such as the mean, variance, or autocovariance—change over time. In a stationary series, these properties are constant and the process’s behavior does not depend on the time at which it is observed. Non-stationarity is common in economic, financial, and environmental data and poses challenges for analysis and forecasting.

Non-stationarity can arise in several forms. A deterministic trend causes the mean to drift over time, while stochastic, or unit-root, non-stationarity causes shocks to have a permanent effect, making the series behave like a random walk. Sometimes both the mean and variance change, and seasonal or structural breaks can contribute.

Implications for analysis are significant. Standard statistical models assume stationarity; non-stationary data can yield spurious relationships in regression and unstable forecasts. Modeling approaches include differencing to achieve stationarity, detrending, or using models that accommodate non-stationarity, such as ARIMA with differencing, or cointegration-based error-correction models when multiple series share a long-term equilibrium.

Tests and diagnosis commonly rely on unit root tests and related procedures. Unit root tests (for example, Augmented Dickey-Fuller or Phillips-Perron) test for stochastic non-stationarity; the KPSS test assesses stationarity around a deterministic trend. Structural-break tests and tests for variance stability can help identify other forms. Knowledge of the data-generating process informs the appropriate method.

Notes: the concept and terminology vary by language; in many contexts non-stationarity is a natural feature of real-world time series. Proper handling is essential for reliable inference and forecasting.