Periodically correlated process (${\gamma }_{t+S}(h)={\gamma }_t(h)$)

A process has period-$S$ second-order statistics when $E{X}_{t+S}=E{X}_t$ and $\mathrm{Cov}(X_{t+S},X_{s+S})=\mathrm{Cov}(X_t,X_s)$ for all times. Its variance can vary by season, so it need not be a weakly stationary process. A periodic covariance period need not be the fundamental period.