Paper: Quantifying and Modeling Long-Range Cross-Correlations in Multiple Time Series with Applications to World Stock Indices

Here’s another econophysics paper from H. Eugene Stanley and crew:  D. Wang, B. Podobnik, D. Horvatić, H. E. Stanley. Quantifying and Modeling Long-Range Cross-Correlations in Multiple Time Series with Applications to World Stock Indices.  In my opinion, the primary contribution of the paper isn’t really their method.  The "global factor model" seems like the same logic found in my paper and T. Conlon’s paper (both of which were submitted under Stanley’s supervision of Physica A).  Furthermore, the claim that the algorithm can be used predictively suffers from the same out-of-sample adjustment issue I’ve seen a hundred times in econophysics.  Oh well, it seems like duplication and poor literature reviews are a staple in econophysics anyway.

But back to the out-of-sample issue, here’s an aside on the point: you cannot perform z-score normalization over a population until you have observed the entire population!  Regardless of whether you normalize each new sample on observed values, or double your storage requirements and re-normalize the entire vector of observations at each step, these values will not necessarily be the same as the population-conditioned z-scores.  You can only appeal to this logic in an approximate sense if you are confident that the distribution you are sampling has constant mean and standard deviation on your sampling frequency (hint: in finance at daily or sub-daily frequency, IT DOESN’T).  

OK, back to the paper.  In my opinion, the primary contribution is the breadth of indices that they used.  An N of 48 in global market indices will get you a pretty comprehensive sample of capitalization and geography.  However,  on this point, there seems to be little-to-no discussion of how these markets behave specifically.  The caption on Figure 6 is the most information I found, and it’s buried on the last page of the paper without labels.  This is still a pre-print, but I hope the paper will still see improvements before its inevitable publication and acceptance in Physica A.