[R-SIG-Finance] A question on volatility

[Paul Ringseth]

Hi:

You really need to jointly estimate the correlations with the variances.  The easiest technique (but not the best) is Orthogonal GARCH from Carl Alexander's papers (http://www.carolalexander.org/publish/download/DiscussionPapers/OrthogonalGARCH_Primer.pdf ).  Recently Engle has recommended a factor DCC-GARCH variant using a heuristic, he calls the MacGyver technique, for large covariance matrices (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1293628 ).    Then Engle, Shephard and Sheppard came up with an exceptionally interesting technique for fitting all parameters in any large covariance matrix http://www.economics.ox.ac.uk/Research/wp/pdf/paper403.pdf -- the estimator is essentially the sum of the quasi-MLE's of all pairs.  Also you should check out Engle's new book -- Anticipating Correlations ( http://press.princeton.edu/titles/8768.html ).    

Whatever you end up doing, you should backtest and compare to published results, for example at Engle's volatility lab -- http://vlab.stern.nyu.edu/analysis .

But as long as the dimensionality of the desired correlation / covariance matrix is not too large ( <= 16 should be ok ), a straightforward DCC-GARCH fit should work.  Here's some R code:

http://www.r-project.org/conferences/useR-2008/slides/Nakatani.pdf 

Cheers -- Paul

-----Original Message-----
From: r-sig-finance-bounces at r-project.org [mailto:r-sig-finance-bounces at r-project.org] On Behalf Of Megh Dal
Sent: Wednesday, October 05, 2011 12:15 PM
To: r-sig-finance at stat.math.ethz.ch
Subject: [R-SIG-Finance] A question on volatility

Dear all, I was trying to understand the correlation among the volatilities in different financial market, however am in dilemma what could be the rightful and acceptable-to-everyone approach. I thought to estimate the volatilities of individual markets using some GARCH modeling, then just calculate the correlation coefficient on the estimated time series of estimated daily volatilities. 

Is it correct approach to understand the correlation? Can somebody point me any online paper or any idea on the same?

Thanks for your time.

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