# autocovariance function

Let $\{X_{t}\mid t\in T\}$ be a stochastic process such that $\operatorname{Var}[X_{t}]<\infty$ $\forall t\in T$. The autocovariance function of $\{X_{t}\}$ is

 $\displaystyle\gamma_{X}(r,s)$ $\displaystyle:=$ $\displaystyle\operatorname{Cov}(X_{r},X_{s})$ $\displaystyle=$ $\displaystyle{E}\big{[}(X_{r}-{E}[X_{r}])(X_{s}-{E}[X_{s}])\big{]}\hskip 28.45% 2756pt\forall r,s\in T.$
Title autocovariance function AutocovarianceFunction 2013-03-22 15:10:08 2013-03-22 15:10:08 CWoo (3771) CWoo (3771) 10 CWoo (3771) Definition msc 60G10 covariance kernel