Weakly stationary process

A weakly stationary process has constant finite mean and covariance depending only on lag.

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.

White noise has constant mean, constant variance, and zero autocovariance at every nonzero lag. Gaussian white noise additionally has jointly Gaussian coordinates and is therefore independent across time.