autocovariance function

Let $\{X_t\mid t\in T\}$ be a stochastic process such that $\forall t\in T$. The autocovariance function of $\{X_t\}$ is

${\gamma }_X(r,s)$ $:=$ $\mathrm{Cov}(X_r,X_s)$

$=$ $E\left[(X_r-E[X_r])(X_s-E[X_s])\right]\mathit{\hspace{1em}\hspace{1em}\hspace{0.5em}\hspace{1em}}\forall r,s\in T.$

Title	autocovariance function
Canonical name	AutocovarianceFunction
Date of creation	2013-03-22 15:10:08
Last modified on	2013-03-22 15:10:08
Owner	CWoo (3771)
Last modified by	CWoo (3771)
Numerical id	10
Author	CWoo (3771)
Entry type	Definition
Classification	msc 60G10
Synonym	covariance kernel