[R-sig-finance] correlation between two stock market indices

[Vadim Ogranovich]

Thank you Patrick! This makes a lot of sense. If I understand you
correctly you are talking about time-varying "instantaneous" correlation
(more precisely covariance) matrix and that a good GARCH can capture the
variations.

Thanks,
Vadim

> -----Original Message-----
> From: Patrick Burns [mailto:patrick at burns-stat.com] 
> Sent: Tuesday, August 31, 2004 4:22 PM
> To: Vadim Ogranovich; r-sig-finance
> Subject: Re: [R-sig-finance] correlation between two stock 
> market indices
> 
> Yes, we are talking about cross-correlation.  (Before we get 
> in an even deeper muddle: for those who can't relate to 
> cross-correlation, ignore it and just think of correlation.)
> 
> I can't think of a very good reference at the moment -- maybe 
> someone else has ideas.
> 
> My statement mainly rests on the following assertion:
> 
> Multivariate GARCH is a reasonably good model for the 
> variance matrix of the returns of assets.
> 
> This is most true of daily data.  Lower frequency data smooth 
> out some of the garchiness; things get complicated with intraday data.
> 
> More specifically the assertion should be that there exists 
> some multivariate GARCH model which is reasonably good.  
> There will be many GARCH models which are not good.  One 
> particular model that almost surely will not be at the head 
> of the class is a constant correlation model.  These were 
> created because of the ease of estimation rather than from 
> any empirical or theoretical motivation.
> 
> If you think of CAPM with the market being modeled as GARCH, 
> then assets will be more highly correlated with each other 
> when the market is in a high volatility period than when it 
> is in a low volatility period.
> 
> Assuming you can believe that correlations change over time 
> (with some form of continuity), then it shouldn't be too much 
> of a leap to believe that the time horizon of interest will 
> influence your estimation procedure.
> 
> If you knew that GARCH were the correct model, then it would 
> be optimal (in the estimation sense) to use GARCH for all 
> time horizons.  But as the time horizon gets longer, all of 
> the estimates approach the unconditional correlation.  So for 
> long time horizons there is not much sense in going through 
> the work of fitting a multivariate GARCH model when you will 
> just end up with the sample correlation anyway.  The more 
> steps you predict ahead, the more model risk you take.  GARCH 
> is not exactly correct, so there is definitely model risk to be had.
> 
> For short time horizons, the model doesn't have to be so 
> perfect in order to outperform the sample correlation.
> 
> Assuming that you don't have multivariate GARCH available to 
> you, there are some half-way measures for getting at 
> predictions for short time horizons.
> A practical option is to use exponential smoothing. 
> 
> Patrick Burns
> 
> Burns Statistics
> patrick at burns-stat.com
> +44 (0)20 8525 0696
> http://www.burns-stat.com
> (home of S Poetry and "A Guide for the Unwilling S User")
> 
> Vadim Ogranovich wrote:
> 
> >>*)  How correlation should be estimated depends on the use 
> to which it 
> >>will be put.  If the time horizon of interest is long -- on 
> the order 
> >>of two months or longer, then an ordinary sample correlation should 
> >>suffice.
> >>If the time horizon is short -- a day or a week, then a 
> GARCH model is 
> >>going to be appropriate.
> >>    
> >>
> >
> >To my embarrassment I do not understand this (we are talking 
> about the 
> >cross-correlation, aren't we?). Is there a paper I could consult to 
> >close this gap in my education?
> >
> >Thank you,
> >Vadim
> >
> >  
> >
> 
> 
>