Autocovariance is Autocorrelation by Variance

Theorem
Let $\map S z$ be a stochastic process giving rise to a time series $T$.

Let $S$ be weakly stationary of order $2$ or greater.

Let $\gamma_k$ denote the autocovariance coefficient of $S$ at lag $k$.

Let $\rho_k$ denote the autocorrelation coefficient of $S$ at lag $k$.

Then:
 * $\gamma_k = \rho_k \sigma_z^2$

where $\sigma_z^2$ denotes the variance of $S$.

Proof
Hence the result.