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

Let $S$ be a stochastic process giving rise to a time series $T$.

The autocorrelation of $S$ at lag $k$ is defined as:

$\rho_k := \dfrac {\expect {\paren {z_t - \mu} \paren {z_{t + k} - \mu} } } {\sqrt {\expect {\paren {z_t - \mu}^2} \expect {\paren {z_{t + k} - \mu}^2} } }$


$z_t$ is the observation at time $t$
$\mu$ is the mean of $S$
$\expect \cdot$ is the expectation.