\begin{definition}[Definition:Autocorrelation]
Let $S$ be a stochastic process giving rise to a time series $T$.
The '''autocorrelation''' of $S$ at lag $k$ is defined as:
:$\rho_k := \dfrac {\expect {\paren {z_t - \mu} \paren {z_{t + k} - \mu} } } {\sqrt {\expect {\paren {z_t - \mu}^2} \expect {\paren {z_{t + k} - \mu}^2} } }$
where:
:$z_t$ is the observation at time $t$
:$\mu$ is the mean of $S$
:$\expect \cdot$ is the expectation.
\end{definition}