the correlation matrix is so large (50000by50000) that it is not efficient in calculating what I want. What I want to do is to break it down to groups and treat each as separate correlation matrices. However, how do I deal with the dependence between those smaller correlation matrices? I have been researching online all day but nothing comes up. There should be some algorithm out there that is related to the approximation of large correlation matrices like this, right?
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Could you be a little more specific about what exactly you're trying to achieve with the matrix? – michaelv2 Jun 16 '11 at 19:19
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to generate 50000*200 dependent variables by multiplying independent random variables by the Cholesky decomposition. – angielovesmath Jun 16 '11 at 20:43
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Even a 4 x 4 correlation matrix is sensitive to errors. In any case, here are some links that might help:
http://www.oxford-man.ox.ac.uk/documents/papers/2011OMI08_Sheppard.pdf
http://www.kevinsheppard.com/images/4/47/Chapter8.pdf
http://arxiv.org/PS_cache/arxiv/pdf/1009/1009.5331v1.pdf
http://cran.r-project.org/web/packages/tawny/index.html
http://www.rinfinance.com/RinFinance2009/presentations/yollin_slides.pdf
http://nurometic.com/quantitative-finance/tawny/portfolio-optimization-with-tawny
http://quantivity.wordpress.com/2011/04/17/minimum-variance-portfolios/
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