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Strict Stationarity


A stochastic process {X_t} is strictly stationary if, for every positive integer m, every collection of times t_1,...,t_m, and every shift h, the random vectors

 (X_(t_1),...,X_(t_m)) and (X_(t_1+h),...,X_(t_m+h))

have the same joint distribution. Thus all finite-dimensional distributions are invariant under a shift of time.

Strict stationarity need not imply weak stationarity unless the required moments exist, and weak stationarity need not imply strict stationarity.


See also

Nonstationary Time Series, Stationary Time Series, Weak Stationarity

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Cite this as:

Weisstein, Eric W. "Strict Stationarity." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StrictStationarity.html

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