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### Definition of stationarity

A random process is strict-sense stationary if the joint distribution of any set of samples does not depend on the sample's placement. Consequently, first order cumulative distribution functions, e.g., mean and variance, of are constant. Furthermore, second order cumulative distribution functions (such as autocorrelation and autocovariance) depend only on the distance in placement, . For example, a Gaussian process is strict-sense stationary since it is completely specified by its mean and covariance function.

If the mean is constant and the autocovariance is a function that depends only on the distance in placement, then we call the data wide-sense stationary or simply stationary. Strict-sense stationary implies wide-sense stationary.

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Stanford Exploration Project
3/8/1999