Stationary Time Series

A stationary time series is a time series whose probabilistic behavior does not change with time. A stochastic process has strict stationarity 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 has weak stationarity, also called covariance stationarity, if

			(2)
			(3)

where denotes the expectation value of . Thus, 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.