# [R-sig-finance] structural breaks in correlation

Achim Zeileis Achim.Zeileis at wu-wien.ac.at
Thu Mar 23 11:26:25 CET 2006

```On Wed, 22 Mar 2006 22:24:51 -0500 Krishna Kumar wrote:

> Hi folks,
>
> I am trying to understand structural breaks in correlation using the
> strucchange package in R.
> I am looking at a rolling window estimate of correlation (pearsons)
> to identify breaks and see if the underlying process has changed.
>
>
>  > data(EuStockMarkets)
>  > dax <- log(EuStockMarkets[,"DAX"])
>  >  ftse <- log(EuStockMarkets[,"FTSE"])
>  > dax.ret<-diff(dax)
>  > ftse.ret<-diff(ftse)
>
> rollingcor <- function(ret, width) {
> T<-dim(ret)[1]
> results<-1:(T-width)
>      for (i in 1:(T-width)) {
>     indx<-i+width
>         results[i] <- cor(ret[i:indx,1],ret[i:indx,2] )
>      }
>      return(results)
>    }
>
>  >dax.ftse.cor<-rollingcor(cbind(dax.ret,ftse.ret),50)

You can compute this quantity much easier via:
dax.ftse.cor <- rapply(diff(log(EuStockMarkets[,c("DAX", "FTSE")])),
50, function(x) cor(x[,1], x[,2]), by.column = FALSE)

>  > ordcus<-efp(dax.ftse.cor~1,type="OLS-CUSUM")
>  > plot(ordcus)
>
> Is this the right way to test a rolling correlation estimate? And are
> there other tests that are recommended besides the cusum test?

I would not use the strategy above, because you introduce a(n
additional) dependence into the series by computing the correlations
beforehand. Instead you could simply use a regression model, e.g.
dax <- diff(log(EuStockMarkets[,"DAX"]))
ftse <- diff(log(EuStockMarkets[,"FTSE"]))
and use a moving estimates test in this regression model, e.g., with a
bandwidth of 10% of the data
me <- efp(dax ~ ftse, type = "ME", h = 0.1)
plot(me, functional = NULL)
which would suggest a shift between 1992-1993 and 1997-1998. Other
tests, not only moving estimates tests would yield similar results, for
example a CUSUM-type test based on the model scores
scus <- gefp(dax ~ ftse)
plot(scus, aggregate = FALSE)
For a recent survey of these and related tests, see
Achim Zeileis (2005). "A Unified Approach to Structural Change Tests
Based on ML scores, F statistics, and OLS residuals," Econometric
Reviews, 24(4), 445-466.
A preprint version is available from my Web page.

hth,
Z

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