Symbols:Greek/Gamma/Autocovariance

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Autocovariance

$\gamma_k$


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.


The $\LaTeX$ code for \(\gamma_k\) is \gamma_k .