[R] CUSUM SQUARED structural breaks approach?

[Rick Ram]

Sorry guys, resending this - none of my posts have gone through
because HTML emails where not being delivered... sending this
plaintext now!

On 28/07/05, Rick Ram <r.ramyar at gmail.com> wrote:
> Hi all,
>  
> I have not looked at this CUSUM SQUARED issue since the emails at the
> beginning of the year but am looking at it again.  For those who are
> interested the following paper gives critical values where n>60 in addition
> to the ones in Durbin 1969.  
>  
> Edgerton, David & Wells, Curt, 1994. "Critical Values for the Cusumsq
> Statistic in Medium and Large Sized Samples," Oxford Bulletin of Economics
> and Statistics, Blackwell Publishing, vol. 56(3), pages 355-65. 
>  
>  
> All the best,
>  
> R.
> 
> On 12/01/05, Achim Zeileis <Achim.Zeileis at wu-wien.ac.at> wrote: 
> > On Tue, 11 Jan 2005 19:33:41 +0000 Rick Ram wrote:
> > 
> > > Groundwork for the choice of break method in my specific application 
> > > has already been done - otherwise I would need to rework the wheel
> > > (make a horribly detailed comparison of performance of break
> > > approaches in context of modelling post break)
> > >
> > > If it interests you, Pesaran & Timmerman 2002 compared CUSUM Squared, 
> > > BaiPerron and a time varying approach to detect singular previous
> > > breaks in reverse ordered financial time series so as to update a
> > > forecasting model.
> > 
> > Yes, I know that paper. And if I recall correctly they are mainly 
> > interested in modelling the time period after the last break. For this,
> > the reverse ordered recursive CUSUM approach works because they
> > essentially look back in time to see when their predictions break down.
> > And for their application looking for variance changes also makes sense.
> > The approach is surely valid and sound in this context...but it might be
> > possible to do something better (but I would have to look much closer at 
> > the particular application to have an idea what might be a way to go).
> > 
> > > This works "fine" i.e. the plot looks correct.  The problem is how to
> > > appropriately normalise these to rescale them to what the CUSUM 
> > > squared procedure expects (this looks to be a different and more
> > > complicated procedure than the normalisation used for the basic
> > > CUSUM).  I am from an IT background and am slightly illiterate in
> > > terms of math notation... guidance from anyone would be appreciated
> > 
> > I just had a brief glance at BDE75, page 154, Section 2.4. If I
> > haven't missed anything important on reading it very quickly, you just
> > need to do something like the following (a reproducible example, based
> > on data from strucchange, using a notation similar to BDE's):
> > 
> > ## load GermanM1 data and model
> > library(strucchange)
> > data(GermanM1)
> > M1.model <- dm ~ dy2 + dR + dR1 + dp + ecm.res + season
> > 
> > ## compute squared recursive residuals
> > w2 <- recresid(M1.model, data = GermanM1)^2
> > ## compute CUSUM of squares process
> > sr <- ts(cumsum(c(0, w2))/sum(w2), end = end(GermanM1$dm), freq = 12) 
> > ## the border (r-k)/(T-k)
> > border <- ts(seq(0, 1, length = length(sr)),
> >             start = start(sr), freq = 12)
> > 
> > ## nice plot
> > plot(sr, xaxs = "i", yaxs = "i", main = "CUSUM of Squares") 
> > lines(border, col = grey(0.5))
> > lines(0.4 + border, col = grey(0.5))
> > lines(- 0.4 + border, col = grey(0.5))
> > 
> > Instead of 0.4 you would have to use the appropriate critical values
> > from Durbin (1969) if my reading of the paper is correct. 
> > 
> > hth,
> > Z
> > 
> > > Does anyone know if this represents some commonly performed type of
> > > normalisation than exists in another function??
> > >
> > > I will hunt out the 1969 paper for the critical values but prior to 
> > > doing this I am a bit confused as to how they will
> > > implemented/interpreted... the CUSUM squared plot does/should run
> > > diagonally up from left to right and there are two straight lines that
> > > one would put around this from the critical values.  Hence, a 
> > > different interpretation/implementation of confidence levels than in
> > > other contexts.  I realise this is not just a R thing but a problem
> > > with my theoretical background.
> > >
> > >
> > > Thanks for detailed reply! 
> > >
> > > Rick.
> > >
> > >
> > > >
> > > > 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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> > > > >
> > > >
> > >
> > 
> 
>