Covariance Function

Covariance Function

In probability theory and statistics, covariance is a measure of how much two variables change together and the covariance function describes the variance of a random variable process or field. For a random field or stochastic process Z(x) on a domain D, a covariance function C(x, y) gives the covariance of the values of the random field at the two locations x and y:

The same C(x, y) is called autocovariance in two instances: in time series (to denote exactly the same concept, where x is time), and in multivariate random fields (to refer to the covariance of a variable with itself, as opposed to the cross covariance between two different variables at different locations, Cov(Z(x₁), Y(x₂))).