I agree with Pat. Time varying correlations in a multivariate GARCH model

are different from the correlations between volatility series. Because

volatility is "unobservable" (i.e, except for special cases like the VIX)

and derived measures like implied volatility are model based (e.g. derived

from Black-Scholes) it is not straightforward to define and measure

correlations between volatilities. One model-based approach in which

volatility is a random variable is the stochastic volatility model. One can

build multivariate models in which the correlation to volatility shocks is

parameterized (but this is not the correlation between volatilities). GARCH

models produce very noisy estimate of volatility and so the correlations

computed from GARCH volatilities are likely to be very noisy as well. A

better approach would be to compute volatilities using intra-day high

frequency data (e.g. realized volatility) - see the realized package. This

would give you much more precise estimates of volatility. Then the problem

would be to model the correlation between the observed volatilities. For

example, simple EWMAs. One could even consider a simple vector

autoregressive model for a multi-variate time series of volatilities. This

is what Andersen, Bollerslev, Diebold and Labys did in their Econometrica

paper. One potential problem is that the realized volatility series tend to

be non-stationary. Just some thoughts.

-----Original Message-----

From:

[hidden email]
[mailto:

[hidden email]] On Behalf Of Patrick Burns

Sent: Wednesday, October 05, 2011 1:39 PM

To:

[hidden email]
Subject: Re: [R-SIG-Finance] A question on volatility

Paul,

If my understanding of Megh's question is correct,

then you've misinterpreted it. I think the

correlations that are being sought are the correlations

between the volatilities of the assets, not the

correlations of the asset returns.

In any case, I'll attempt to give a bit of an answer

to the question as I understand it.

I'm uneasy about correlation of volatilities because

they are quite skewed. Certainly favor rank correlations

over Pearson correlation.

Somewhere in Engle's body of work is a paper (or more)

on the transmission of volatility. I don't recall

at all what the technique was, and vaguely remember

it being a mildly satisfying answer.

On 05/10/2011 21:10, Paul Ringseth wrote:

> 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:

[hidden email]
[mailto:

[hidden email]] On Behalf Of Megh Dal

> Sent: Wednesday, October 05, 2011 12:15 PM

> To:

[hidden email]
> 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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>

--

Patrick Burns

[hidden email]
http://www.burns-stat.comhttp://www.portfolioprobe.com/blogtwitter: @portfolioprobe

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