Category:Definitions/Autocovariance

This category contains definitions related to Autocovariance.
Related results can be found in Category: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.