@Rick, thanks for sharing… I will definitely have to read that!

In that method we step backwards through the Cornish Fisher Expansion to the normal distribution to arrive at the vector length or penalty function used Value at Risk calculations but allowing to solve for the higher moments of skewness and kurtosis also. In risk these can be thought of as additional positive or negative risk penalty vectors but ones which interact with each other. The difficulty here is that in the multivariate setting the interaction embeds the weighting as well where we would ideally like a weight independent solution.

In essence we are treating the skewness as an additional positive or negative vector length and the kurtosis as a change in angle. We cheat by Woking backwards from the univariate solution but have to recalculate the modified correlation matrix each time the weights change which is very computationally expensive. I wonder if you can think of a more elegant global satisfying solution ?

May not be possible since we are essentially trying to reduce a 4dim problem to a 2dim one.

If you know the two correlations of one time series with two other predictor time series, what does this tell you about the possible range of correlation between the two predictor time series. That is, given r(X,Y)=a and r(X,Z)=b, what is the possible range of r(Y,Z)=c in terms of a and b?

Of course some examples are intuitively trivial (eg, if a=b=1, then c=1, and if a=0 but b=1 then c=0). But, consider if a=b=.7 (which are strong correlations), then I think the possible range of c is still enormous (0.<c<1. ). In this case, I reasoned because X accounts for half the variance of Z and Y accounts for half the variance of Z that X could possibly account for the same half of the variance as Y (ie c=r(X,Y)=1). Or, X could account completely for the other half of the variance that is not accounted for by Y but together X and Y account for all of the variance of Z (ie c=r(X,Y)=0). This understanding has, for instance, implications for (over) interpreting causality based on empirical evidence.

Despite all that I’ve found the increasing need for understanding statistics (as you work on/with statistical classifiers and you feel the need to really ‘get’ those s.o.b.s for only then do you have a chance at reasoning why they fail on you the way they do) and your piece just made a bit of my brain drop a quarter — I’m Dutch; comprehension is so precious around here we are willing to part with a quarter instead of only a penny