Covariance-stationary

A process <math>X_t<math>is said to be covariance-stationary (or weakly stationary), if

<math>\mbox{E}(X_t)=\mu \quad\forall t \,<math>

<math>\mbox{E}(X_t-\mu)(X_{t-j}-\mu)=\gamma_j \quad \forall t \mbox{ and any }j \,<math>,

where <math>\gamma_j<math> denotes the autocovariance. Thus, a process is covanriance-stationary, if neither the mean nor the autocovariances depende on the date <math>t<math>.