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

[Patrick Burns]

I'll summarize what I see as the key points -- most of which have
already been covered.

*)  You want to have the correlation of the returns, not the prices.
Hence you want a command similar to:

rets <- diff(log(prices))

*)  You need to be careful of asynchronous data.  In this case there
is no problem since both are American.

*)  There is minimal autocorrelation in financial returns of liquidly
traded assets.  That should be close to the least of your worries
about getting the model wrong.

*)  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. 

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")

Christoph Lehmann wrote:

> Dear finance professionals
>
> As I was asked by a friend, whether we can compute the correlation 
> between two stock market indices (e.g. NASDAQ index and Dow Jones 
> index), and I am unfortunately NOT an expert in finance:
>
> (1) What model would you recommend for this kind of question?
>
> something like:
>
> library(ts)
> arima(x, order=???, xreg=y)
>
> library(nlme)
> gls(x~y,correlation=corARMA(p=?,q=?))
>
> what would you recommend, and what about the "?" :)
>
> (2) Furthermore, searching the web, I found, that (sorry, you experts 
> certainly know this, but I have no experience with financial data), 
> usually the time series are uncorrelated, but show strong "ARCH 
> effects", ie., are not independent.
>
> Does this mean, that any kind of correlation analysis with stock market
> indices is senseless, since maybe we don't get a sign. correlation, 
> but this doesn't mean that the series are independent?
>
> Many thanks for your help
>
> Chris
>
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