Re: Volatilities and correlation

On Sat, 26 May 2007 00:26:49 EDT, Yves <sunder_1600@xxxxxxxxx> wrote:

Given 2 distributions, it is possible for each of the volatilities to change, and for the correlation to not change. Why?

Why do you ask? What are you asking about, in real life?
I suppose, if you are throwing away cases to change the
volatilities, it depends on how you select the cases.
(Folks have not been using that term here, but I assume that
the volatilities are the variances.)

If you select a sample with restricted range on a variable,
you do expect a smaller correlation - when you are measuring
something that has a bivariate normal correlation in the
population. However, real samples may happen in all sorts
of shapes. Some people occasionally speak of correlations
that are "attenuated" by the narrow range. (There is also
attenuation for reliability, which is a more general idea.)

If you throw away bivariate outliers, you can increase
the correlation while decreasing variances.

So, what happens to the correlation depends on which cases
you throw away. Or edit the values of.

--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.

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