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
covariance matrix	Failed to parse (Cannot write to or create math output directory): \gamma_{XY}(n,m) =E[ (X_n-E[X_n])\,(Y_m-E[Y_m])]

where σ_X and σ_Y are the standard deviations of the {X_i} and {Y_i} respectively. Notably, correlation is dimensionless while covariation is in units obtained by multiplying the units of each variable. The correlation and covariance of a variable with itself (i.e. Y = X) is called the autocorrelation and autocovariance, 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
cross covariance