Stationary process

Summary

A stationary process is a stochastic process whose statistical behaviour does not change under shifts of time. All its finite-dimensional distributions are invariant under a common time shift. A weaker notion, weak or wide-sense stationarity, asks only that the mean be constant and the covariance depend only on the time lag. Stationary processes are the basic models of time series analysis and of ergodic theory, and their covariance has a spectral representation by the Wiener–Khinchin theorem.