Autocovariance ($\gamma (h)$)

The autocovariance at lag $h$ is $\gamma (h)=\mathrm{Cov}(X_{t+h},X_t)$, independent of $t$ for a weakly stationary process.

The autocorrelation function is $\rho (h)=\gamma (h)/\gamma (0)$ when $\gamma (0)>0$.

The sample autocorrelation function replaces the mean and lagged covariance in $\rho (h)$ by their empirical counterparts.