What is "autocovariance"

n. (context statistics English) The covariance of a signal with another part of the same signal

In probability theory and statistics, given a stochastic process X = (X), the autocovariance is a function that gives the covariance of the process with itself at pairs of time points. With the usual notation E for the expectation operator, if the process has the mean function μ = E[X], then the autocovariance is given by

C(t, s) = cov(X, X) = E[(X − μ)(X − μ)] = E[XX] − μμ. 

Autocovariance is related to the more commonly used autocorrelation of the process in question.

In the case of a multivariate random vector X = (X, X, ..., X), the autocovariance becomes a square n by n matrix, C, with entry i, j given by C(t, s) = cov(X, X) and commonly referred to as the autocovariance matrix associated with vectors X and X.