I'm reading two papers by Mark Kritzman on two indicators (turbulence proxied by the Mahalanobis distance and absorption ratio which is basically the ratio of the variance captured by the top 20% PCA components), with formulas below:
Turbulence: $$ d_t = (y_t - \mu) * \Sigma^{-1} * (y_t - \mu)' $$
Absorption Ratio:
Notice that both formulas involve estimating a covariance matrix. While reading the original papers of the author, I have the impression that he does not consider any weight when estimating the covariance matrix. However, would it make more sense to include a column weight for each column according to the weight at the start of the estimation period ? For example in the Turbulence measure, considering that he used the data for 10 (now 11) sectors in the S&P 500, wouldn't it make more sense if we include the weights of each sector in the calculations because we are measuring the Turbulence measure for the S&P 500 after all, if we treat every component equally then would it not skew the final measure ?
The question is the same for the absorption ratio.
Thanks for your help.
(edited for math, but edits must be more than 6 characters, thus this notice.)
