AR(1)-GARCH(1,1) regression model

[Marcin P?�ciennik]

Dear Rmetrics Core Team,
I sent this message a couple of times to r-help group but unfortunately did
not get any response that would be helpful...so I decided to write directly
to the maintainer of the package 'fGarch'.


I have a rather complex problem... I will have to explain everything in
detail because I cannot solve it by myself...i just ran out of ideas. So
here is what I want to do:
I take quotes of two indices - S&P500 and DJ. And my first aim is to
estimate coefficients of the DCC-GARCH model for them. This is how I do it:


library(tseries)
p1 = get.hist.quote(instrument = "^gspc",start = "2005-01-07",end =
"2009-09-04",compression = "w", quote="AdjClose")
p2 = get.hist.quote(instrument = "^dji",start = "2005-01-07",end =
"2009-09-04",compression = "w", quote="AdjClose")
p = cbind(p1,p2)
y = diff(log(p))*100
y[,1] = y[,1]-mean(y[,1])
y[,2] = y[,2]-mean(y[,2])
T = length(y[,1])

library(ccgarch)
library(fGarch)

f1 = garchFit(~ garch(1,1), data=y[,1],include.mean=FALSE)
f1 = f1 at fit$coef
f2 = garchFit(~ garch(1,1), data=y[,2],include.mean=FALSE)
f2 = f2 at fit$coef

a = c(f1[1], f2[1])
A = diag(c(f1[2],f2[2]))
B = diag(c(f1[3], f2[3]))
dccpara = c(0.2,0.6)
dccresults = dcc.estimation(inia=a, iniA=A, iniB=B, ini.dcc=dccpara,dvar=y,
model="diagonal")

dccresults$out
DCCrho = dccresults$DCC[,2]
matplot(DCCrho, type='l')


dccresults$out deliver me the estimated coefficients of the DCC-GARCH model.
I had also some questions about this part but it is not connected with the
package 'tseries' so I am not going to ask you for help here.

Ok. This would be it when it comes to DCC-GARCH.

Now, using conditional correlation obtained from the DCC-GARCH model, I want
to test for structural shifts in conditional correlations. To be precise, I
want to test whether the conditional correlations significantly increase in
the turmoil period / during the Subprime crisis.
The regression model is AR(1)-GARCH(1,1), using a dummy variable specified
as:



*** the equations, you can find in the attachment ***



where the first equation is the conditional correlation among the two
indices during the Subprime crisis, Dt is a dummy variable for the turmoil
period, and the second equation (hij,t) is the conditional variance of eij,t

The aim is, of course, to find the estimates of the regression model on
structural shifts in the conditional correlations obtained in the DCC-GARCH
model.

I found an information that there is no function for AR(1)-GARCH(1,1)
regression model. That's why, apparently, it has to be done in two steps:

1) estimate the AR parameters
2) estimate the GARCH part of the model on the residuals from the AR model

And this would be my rather poor idea of how to do it...


library(timeSeries)
library(fSeries)
library(tseries)

step1 = arma(DCCrho, order = c(1,0), include.intercept = TRUE)
step1$res
step11 = na.remove(step1$res)
step2 = garch (step11, order = c(1,1), include.intercept = TRUE)


To be honest I have no clue how whther it is correct. I do not even now why
do I get a missing value as a result of step1 (step1$res[1]) and how to
account for it? Above, I just removed it but then I have a smaller number of
observations...and this is probably wrong.
And then these GARCH estimates on the residuals...does the code for that
make sense at all?


I also had another idea, to apply the following code instead of the one
written above:

garchFit(formula = ~ arma(1,0) + garch(1,1), data=DCCrho, include.mean=TRUE)

But I am not sure if this is delivering me the coefficients I am looking
for.

Hopefully, you will find time to give me a hand because I have to solve the
problem and I reached the point where I cannot move forward without
someone's help.

Thank you very much in advance for looking at/checking what I wrote and
helping me.

Best regards
Marcin Płóciennik
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://stat.ethz.ch/pipermail/rmetrics-core/attachments/20110524/4c4b40f5/attachment-0001.html>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Equations.pdf
Type: application/pdf
Size: 47651 bytes
Desc: not available
URL: <https://stat.ethz.ch/pipermail/rmetrics-core/attachments/20110524/4c4b40f5/attachment-0001.pdf>