Stacionaarsus

Stacionaarsus refers to a property of a time series where its statistical characteristics, such as mean, variance, and autocorrelation, do not change over time. A time series is considered strictly stationary if its probability distribution remains the same for any time shift. More commonly, a time series is considered weakly stationary if its mean and variance are constant over time, and its autocorrelation depends only on the time lag between observations, not on the specific time points. This means that the random fluctuations around the mean are consistent throughout the series.

The concept of stationarity is crucial in time series analysis because many statistical models, particularly those based on autoregression and moving averages, assume that the underlying data generating process is stationary. If a time series is not stationary, it often needs to be transformed into a stationary one before these models can be applied effectively. Common methods for achieving stationarity include differencing, where the difference between consecutive observations is taken, or transformations like logarithmic or square root transformations to stabilize variance. Identifying stationarity or non-stationarity is typically done through visual inspection of time series plots and autocorrelation functions, as well as statistical tests like the Augmented Dickey-Fuller (ADF) test or the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test.