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The autocovariance of a random process X(t), also called covariance function, is defined as:

CX(t1,t2) = E{ (X(t1) - EX(t1)) (X(t2) - EX(t2)) }

where E denote the expectation. The autocovariance is also given by:

CX(t1,t2) = RX(t1,t2) - EX(t1)EX(t2)

where RX(t1,t2) denotes the autocorrelation of the random process.

The autocovariance of a sequence of random variables is thus an extension of the concept of variance and covariance. See also covariance matrix, which can be seen as a sampling of the 2-D autocovariance function.

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