Correlation and convolution (function or number)

[pinsky]

Hy.

I have a problem about correlation depending whether it it observed as a measurement of linear fit of statistical data, and when observed as a relationship between two continuous functions.

Is a result of correlation a coefficient (Pearson's product-moment coefficient) or a function?
If the correlation is a number, what information does a autocorrelation correlogram represent?

And if correlation is a number, why is convolution a function then?

tnx

 

[mathman]

A correlation is a relationship between a pair of random variables.

If these are stand alone, it is a number.

If the random variables are elements of a stochastic process, the the correlation will be a function of the parameters of the stochastic process.

If the random variables are terms in the same stochastic process, then the correlation is an auto-correlation function.

A convolution is a particular kind of integration process. The result may be a correlation, depending on what functions are involved.