stationariteitvoorwaarde

Stationariteitvoorwaarde refers to a condition in time series analysis where the statistical properties of a time series, such as its mean, variance, and autocorrelation, remain constant over time. A stationary time series is one whose behavior is predictable in the long run because its underlying statistical structure does not change.

There are several types of stationarity. Strict stationarity means that the entire probability distribution of the time series is invariant over time. However, this is a very strong condition and often difficult to verify. A more commonly used and practical concept is weak stationarity, also known as covariance stationarity. For a time series to be weakly stationary, it must satisfy three conditions: its mean is constant, its variance is constant, and the autocovariance between any two time points depends only on the time lag between them, not on the actual time points themselves.

Non-stationary time series often exhibit trends, seasonality, or a changing variance, which can complicate statistical modeling and forecasting. Many time series models, such as ARIMA (Autoregressive Integrated Moving Average) models, assume stationarity. If a time series is not stationary, it often needs to be transformed to achieve stationarity before applying these models. Common transformation techniques include differencing, taking logarithms, or seasonal adjustment. Detecting non-stationarity can be done through visual inspection of plots (e.g., time series plots, autocorrelation plots) or through statistical tests like the Augmented Dickey-Fuller (ADF) test.