Symbols:Greek/Rho/Autocorrelation
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Autocorrelation
- $\rho_k$
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.
The $\LaTeX$ code for \(\rho_k\) is \rho_k
.