Definition:Autocorrelation

Definition
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.

Also known as
Autocorrelation is also known as serial correlation.