structural breaks in correlation

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