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

Pfaff, Bernhard Bernhard.Pfaff at drkw.com
Mon Aug 30 11:56:01 CEST 2004


> > 
> > Many thanks, Bernhard!
> > 
> > What do you think about the suggestion, made by another 
> list member, 
> > that I can just compute the correlation for the differentiated data 
> > between the two stock market index series, with no control for 
> > autocorrelation, etc, since according to the effective market 
> > hypothesis 
> > stock market index series don't show autocorrelation at all?
> 
well, here you are superimposing the validity of a 
hypothesis, that should be checked first. By using 
differenced data you are almost always on the *safe side*, 
but again you are giving up the information content of the 
series in levels. This can be circumvented by specifying an 
ECM. Furthermore, you might want to use log data, i.e. a 
transformation that stabilises the variance. As a side effect 
the lm() estimated coefficients can be interpreted as 
elasticities, i.e. the responsiveness of your lhs-variable to 
a unit change of your rhs-variable (in levels).

> 
> > 
> > I think, I will just check, if there isn't an 
> > autocorrelation, checking 
> > acf and pacf, as you suggested. Thanks a lot.
> 
yes, and this tells you the order to specify for arma(), 
given a stationary series:

ar(p): slowly decaying acf (or dampening alternating in case 
of negative ar coeffcient) and a spike at p in the pacf.

ma(q): just like ar(p), but the shape of acf and pacf are 
reversed, i.e. single peak in the acf and slowly decaying 
pacf (or dampening alternating in case of negative ma coeffcient).

HTH,
Bernhard

> 
> > 
> > Cheers
> > 
> > Christoph
> > 
> > Pfaff, Bernhard 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:
> > > 
> > > 
> > > Hello Christoph,
> > > 
> > > you can almost always compute correlations, if these 
> > calculations make sense
> > > and are meaningful is a different matter :-)
> > > 
> > > 
> > >>(1) What model would you recommend for this kind of question?
> > >>
> > >>something like:
> > >>
> > >>library(ts)
> > >>arima(x, order=???, xreg=y)
> > > 
> > > 
> > > sure, you can do this and choose the appropriate order as 
> > it is outlined by
> > > Box-Jenkins (i.e. check the acf and pacf of the residuals 
> > combined with
> > > diagnostic tests for serial uncorrelatedness). Most likely 
> > you want/have to
> > > work with differenced data, due to the *trending* character 
> > of the ts in
> > > question. The snag is that level information is lost. 
> > Hence, you might want
> > > to specify an ECM / VECM and prior to this check the order 
> > of integration of
> > > the series involved. Relevant packages to accomplish this 
> > would be ts,
> > > tseries, dse and urca; to my knowledge (check
> > > http://www.mayin.org/ajayshah/KB/R/R_for_economists.html 
> > for an overview). 
> > > 
> > > 
> > >>library(nlme)
> > >>gls(x~y,correlation=corARMA(p=?,q=?))
> > >>
> > >>what would you recommend, and what about the "?" :)
> > > 
> > > 
> > > this would apply if the *error term* is not nicely behaved 
> > and would follow
> > > as a second step, hence after checking the residuals from a 
> > simple lm() or
> > > arima(), as is described from ?gls
> > > 
> > > Description:
> > > 
> > >      This function fits a linear model using generalized 
> > least squares.
> > >      The errors are allowed to be correlated and/or have unequal
> > >      variances.
> > > 
> > > As a side note, in econometrics it is common notation that 
> > the response is
> > > named 'y' and the predictor 'x' and not vice versa.
> > > 
> > > 
> > >>(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.
> > > 
> > > 
> > > ARCH refers to the behaviour of the variance of the error term
> > > (autoregressive conditional heteroskedasticity). Again, 
> > check the residuals
> > > first, if ARCH is prevailent and only then estimate an 
> > ARCH, GARCH etc. type
> > > of model. Note, uncorrelatedness and independence are only 
> > equivalent in
> > > case of normality. The former does not imply the latter, 
> > only if the the
> > > series are normally distributed. But if two series are 
> > independent then
> > > these series are also uncorrelated.
> > > 
> > > A last side note, ask yourself what the model's aim is. 
> > What should the
> > > model explain? What's it purpose? After having answered 
> > these questions, you
> > > can pick one of methods and not blindly apply either one of them.
> > > 
> > > HTH,
> > > Bernhard
> > > 
> > > 
> > > 
> > >>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
> > >>
> > >>_______________________________________________
> > >>R-sig-finance at stat.math.ethz.ch mailing list
> > >>https://stat.ethz.ch/mailman/listinfo/r-sig-finance
> > >>
> > > 
> > > 
> > > 
> > > 
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> 


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