Cross-correlation matrix: Difference between revisions

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A '''correlation function''' is a statistical [[correlation]] between [[random variable]]s at two different points in space or time, usually as a function of the spatial or temporal distance between the points. If one considers the correlation function between random variables representing the same quantity measured at two different points then this is often referred to as an [[autocorrelation function]] being made up of [[autocorrelation]]s. Correlation functions of different random variables are sometimes called '''cross correlation functions''' to emphasise that different variables are being considered and because they are made up of [[cross correlation]]s.

Correlation functions are a useful indicator of dependencies as a function of distance in time or space, and they can be used to assess the distance required between sample points for the values to be effectively uncorrelated. In addition, they can form the basis of rules for interpolating values at points for which there are no observations.

Correlation functions used in [[correlation function (astronomy)|astronomy]], [[financial analysis]], and [[statistical mechanics]] differ only in the particular stochastic processes they are applied to. In [[quantum field theory]] there are [[Correlation function (quantum field theory)|correlation functions over quantum distributions]].