Definition:Autocovariance

Definition
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.