*X*(

*t*), also called covariance function, is defined as:

C_{X}(t_{1},t_{2}) = E{ (X(t_{1}) - EX(t_{1})) (X(t_{2}) - EX(t_{2})) }

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

C_{X}(t_{1},t_{2}) = R_{X}(t_{1},t_{2}) - EX(t_{1})EX(t_{2})

where R_{X}(*t*_{1},*t*_{2}) 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.