Stacionaritást

Stacionaritást is a term used in statistical analysis, particularly in time series analysis, to describe a particular property of a stochastic process. A time series is considered stationary if its statistical properties, such as its mean, variance, and autocorrelation, do not change over time. This means that the underlying generating process of the data remains constant.

There are different types of stationarity. Strict stationarity requires that the joint probability distribution of any set of observations remains the same over time, regardless of when the observations are taken. However, this is a very strong condition and is rarely met in practice. A more commonly used and practical definition is weak stationarity, also known as covariance stationarity. For a process to be weakly stationary, its mean must be constant, its variance must be finite and constant, and the autocovariance between any two time points must depend only on the time lag between them, not on the specific time points themselves.

Many statistical methods for time series analysis, such as ARIMA models, assume that the data is stationary. If a time series is not stationary, it often needs to be transformed, for example by differencing, to achieve stationarity before applying these methods. Detecting stationarity is an important step in time series analysis, and various statistical tests, like the Augmented Dickey-Fuller test, are used for this purpose. Non-stationary series often exhibit trends, seasonality, or changing volatility, which can complicate forecasting and inference.