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

[Patrick Burns]

Precisely.

Vadim Ogranovich wrote:

>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
>
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>>-----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:
>>
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>>
>>>>*)  How correlation should be estimated depends on the use 
>>>>        
>>>>
>>to which it 
>>    
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>>>>will be put.  If the time horizon of interest is long -- on 
>>>>        
>>>>
>>the order 
>>    
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>>>>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
>>>
>>> 
>>>
>>>      
>>>
>>
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