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.