What is the difference between auto-correlation and cross-correlation?

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SUMMARY

The discussion clarifies the distinction between auto-correlation and cross-correlation, emphasizing that the primary difference lies in normalization. Auto-correlation relates to the correlation of a variable with itself over time, while cross-correlation involves the correlation between two different variables. Both types of correlation are derived from their respective co-variances, normalized by the square root of the product of the variances of the individual variables, ensuring that correlation values remain between 0 and 1.

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What is the difference between Auto-correlation and auto-variance?
The same for cross-correlation and cross-variance?
 
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The essential difference in both cases is a matter of normalization. The correlations are obtained from the cross- or co- variances by dividing by the square root of the product of the variances of the individual variables being correlated. As a result the correlations are limited in magnitude to be between 0 and 1.
 

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