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of a stochastic process

The covariance of and . If denotes the mathematical expectation of a random variable , then the autocovariance equals

The term "autocovariance" is usually applied to stationary (in the wide sense) stochastic processes (cf. Stationary stochastic process). For such processes the autocovariance depends only on and differs from the auto-correlation by the presence of a single factor which is equal to the variance of . The terms "covariance function" and "autocovariance function" are used together with the term "autocovariance" .

How to Cite This Entry:
Autocovariance. A.V. Prokhorov (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098