Definition of stationarity

A random process $y({\bf x})$ 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 $y({\bf x})$are constant. Furthermore, second order cumulative distribution functions (such as autocorrelation and autocovariance) depend only on the distance in placement, ${\bf x_2 - x_1}$. 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.