Statiionaarsed

Statiionaarsed is an Estonian term used in science to describe entities, states, or processes whose statistical properties do not change over time. In time-series analysis and probability, statiionaarsed characteristics typically refer to aspects such as constant mean, constant variance, and a time-invariant dependence structure. The concept is central to many modeling approaches, where stationarity ensures that the same statistical rules apply across different time periods.

There are two primary notions of stationarity commonly discussed. Strict sense stationarity requires that the joint distribution of observations is unchanged by a shift in time. Weak or second-order stationarity requires only that the mean and autocovariance are time-invariant, with the autocovariance depending solely on the time lag between observations. These definitions help determine which mathematical tools and inference methods are appropriate for a given data set.

Examples often cited include white noise, which is typically strictly stationary, and certain autoregressive processes (for instance, an AR(1) process with absolute value of the coefficient less than one), which are weakly stationary. Non-stationary processes include those with trends or unit roots, such as a random walk, where statistical properties evolve over time.

Applications span econometrics, engineering, climatology, and other fields that rely on time-series data. Tests for stationarity, such as unit root tests, help researchers decide whether modeling assumptions are met or if transformations are needed to achieve stationarity before applying standard methods.

In Estonian-language literature, statiionaarsed protsessid or related phrases are used to describe these concepts, with terminology that parallels the broader statistical framework of stationarity.