Covariance and correlation

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Main articles: covariance, correlation.

In probability theory and statistics, the mathematical descriptions of covariance and correlation are very similar. Both describe the degree of similarity between two random variables or sets of random variables.

correlation matrix	[\phi_(n,m) =E[ X_n-E[X_n],Y_m-E[Y_m]]]
covariance matrix	[\gamma_(n,m) =E[ (X_n-E[X_n]),(Y_m-E[Y_m])]]
autocorrelation matrix	[\phi_(n,m) =E[ (X_n-E[X_n])(X_m-E[X_m])]/(\sigma_X \sigma_Y) \;]
autocovariance matrix	[\gamma_(n,m) =E[ (X_n-E[X_n]),(X_m-E[X_m])]]

where [\sigma_X] and [\sigma_Y] are the standard deviations of the [\] and [\] respectively.

In the case of stationarity, the means are constant and the covariance or correlation are functions only of the difference in the indices:

cross correlation	[\phi_(m) =E[ (X_n-E[X_n]),(Y_-E[Y_])]/(\sigma_\sigma})]
cross covariance	[\gamma_(m)=E[ (X_n-E[X]),(Y_-E[Y])]]
autocorrelation	[\phi_(m) =E[ (X_n-E[X_n]),(X_-E[X_])]/(\sigma_X \sigma_Y)]
autocovariance	[\gamma_(m) =E[ (X_n-E[X]),(X_-E[X])]]

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