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

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Auto-correlation measures the correlation of a signal with itself at different time lags, while auto-variance refers to the variance of that signal. Cross-correlation assesses the correlation between two different signals, whereas cross-variance pertains to the variance of those two signals. The key distinction lies in normalization; correlations are derived from cross- or co-variances by dividing by the square root of the product of the variances of the variables involved. This normalization ensures that correlation values range between 0 and 1. Understanding these differences is crucial for accurate data analysis in time series and signal processing.
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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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