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.