\begin{definition}[Definition:Autocovariance]
Let $S$ be a stochastic process giving rise to a time series $T$.
The '''autocovariance''' of $S$ at lag $k$ is defined as:
:$\gamma_k := \cov {z_t, z_{t + k} } = \expect {\paren {z_t - \mu} \paren {z_{t + k} - \mu} }$
where:
:$z_t$ is the observation at time $t$
:$\mu$ is the mean of $S$
:$\expect \cdot$ is the expectation.
\end{definition}