Weak Stationarity

A stochastic process with finite second moments is weakly stationary, or covariance stationary, if its population mean is constant and its covariance depends only on the lag between observations. Thus there are functions and such that

and

for all and .

Weak stationarity does not in general imply strict stationarity. Conversely, strict stationarity implies weak stationarity when the necessary second moments exist.