[R] CUSUM SQUARED structural breaks approach?

[Achim Zeileis]

On Tue, 11 Jan 2005 13:10:51 +0000 Rick Ram wrote:

> Dear all,
> 
> Does anyone know where there is R or S code for the CUSUM SQUARED
> structural breaks approach?   (Brown, Durban and Evans, 1975 - used in
> Pesaran and Timmerman, 2002)

Not to my knowledge.
 
> The problem is that the breaks package

I guess you're referring to the strucchange package. There is no package
breaks, at least not on CRAN.

> only appears to offer the
> standard 'unsquared' CUSUM, even though it appears most think it is
> inferior to the squared version. 

Yes, it's part of the folklore that one should use the CUSUM of squares
rather than the CUSUM test. However, in many scenarios one wouldn't want
to use either test. The BDE CUSUM test is good when you want to know
when 1-step ahead predictions start to break down (and that works only
if the break occurs early in the sample period). The CUSUM of squares
test is more appropriate if you want to detect changes in the variance
(rather than the conditional mean).
For both problems (breaks in the mean / breaks in the variance) there
are other tests which are usually more appropriate than the BDE CUSUM or
CUSUM of squares test which is why I haven't implemented the latter.
(But, of course, no test can be uniformly superior due to the vast
alternative.)

> It might appear to be a relatively
> simple problem - just use the recursive residuals function, square
> them and then take the cumulative sum.  But the problem is that the
> normalisation and calculation of confidence levels is completely
> different.

Yes. Computing the CUSUM of square process is straightforward using the
recresid() methods. To obtain critical values, you will either have to
simulate them or use the tabulated values referenced in BDE from Durbin
(1969).

But depending on the model and hypothesis you want to test, another
technique than CUSUM of squares might be more appropriate and also 
available in strucchange.

hth,
Z

> Any help or pointers about where to look would be more than
> appreciated!  Hopefully I have just missed obvious something in the
> package...
> 
> Many thanks,
> 
> Rick R.
> 
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