stationäärisyys

Stationarity is a fundamental concept in time series analysis. A time series is considered stationary if its statistical properties, such as mean, variance, and autocorrelation, do not change over time. In simpler terms, a stationary time series looks statistically similar regardless of when you observe it.

There are two main types of stationarity: strict stationarity and weak stationarity, also known as covariance stationarity. Strict stationarity requires that the entire joint probability distribution of the time series remains invariant over time. This is a very strong condition and often difficult to satisfy in practice. Weak stationarity is a more relaxed condition and is typically what is meant when referring to stationarity in applied contexts. For a time series to be weakly stationary, its mean must be constant over time, its variance must be constant over time, and the autocovariance between two time points must depend only on the time lag between them, not on their absolute positions in time.

Stationarity is a crucial assumption for many time series models, including autoregressive (AR), moving average (MA), and ARIMA models. These models rely on the assumption that past statistical properties can be used to predict future behavior. If a time series is non-stationary, its statistical properties are evolving, making predictions based on historical data unreliable.

Non-stationarity can manifest in various ways, such as trending behavior (a gradual increase or decrease in the mean), seasonality (patterns that repeat over fixed periods), or heteroscedasticity (changing variance). Techniques like differencing, transformations (e.g., logarithmic transformation), or seasonal adjustment are often employed to make non-stationary time series stationary before applying standard modeling techniques. Detecting non-stationarity can be done through visual inspection of time series plots and autocorrelation functions, as well as through formal statistical tests like the Augmented Dickey-Fuller test.