Correlations and variance?

[Shaddyab]

What is the difference between Auto-correlation and auto-variance?
The same for cross-correlation and cross-variance?

 

[mathman]

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.