The autocovariance of a

random process *X*(

*t*), also called covariance

function, is defined as:

C_{X}(*t*_{1},*t*_{2}) = E{ (*X*(*t*_{1}) - E*X*(*t*_{1})) (*X*(*t*_{2}) - E*X*(*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}) - E*X*(*t*_{1})E*X*(*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.