This is probably a silly question that I should know but I’m a little confused and just wanted to make sure I am clear. The 2009 Level 2 volume 1 book states, “Correlation coefficients can be computed validly if the means and Variances of X and Y, as well as the covariances of X and Y, are finite and constant…when these assumptions are not true, correlations between two different variables can depend greatly on the sample that is used.” Can someone explain what properties the words “finite” and “constant” are referring to? Thanks, appreciate the help
Finite: You can come up with distributions which have infinite or undefined means or variances. In finance, people talk about Levy distributions which have infinite variances (which mean you have a large enough probability of getting a really big move that it makes no sense to talk about volatility). If X or Y has a Levy distribution, it makes no sense to talk about their correlation. Constant: If X and Y have changing distributions then their correlation can change as well. It’s not exactly true that this is required though. Edit: " If X or Y has a Levy distribution, it makes no sense to talk about their correlation" - I guess…
Cauchy distribution is an example of a distribution that doesn’t have a finite variance: http://en.wikipedia.org/wiki/Cauchy_distribution