Stationary Time Series

A stationary time series is a time series whose probabilistic behavior does not change with time. A process is strictly stationary if the joint distribution of

(1)

is the same as that of for every , every choice of times, and every shift .

A process with finite second moments is weakly stationary, also called covariance stationary, if

			(2)
			(3)

so its mean is constant and its covariance depends only on the lag . Strict stationarity does not in general imply weak stationarity unless the necessary moments exist, and weak stationarity does not in general imply strict stationarity.