[R-sig-finance] [R] question about GARCH - newbie question

Patrick Burns patrick at burns-stat.com
Sat Feb 18 18:15:24 CET 2006

I have moved this from R-help to R-sig-finance.  And
I'll let someone else handle some of the R specific

An understanding of the meaning of the coefficients might
be attained by reading the help file.  If not, then a message
to the maintainer of the package with suggests on how to
make the help file more clear would be in order.

Another way of deciding (assuming you have market
return data) is to fit a garch(1,1) model and look at the
coefficients.  The one that is about .9 goes with the lagged
conditional variance, and the one that is about .1 goes
with the lagged squared residual.  By the way, this test is
only likely to work if you have enough data -- a dataset
with 1000 daily returns is a fairly small sample.

Regarding question 2 on model selection:  The not-very-good
common practice is to fit a garch(1,1) and forget about it.
A garch(2,2) model is probably a better choice given a limited
menu.  The adequacy of the model can be checked by using
a rank Ljung-Box test on the squared residuals from the model.
It is important to use the rank rather than the standard test
for this -- see the Burns Statistics working paper on the subject.

Patrick Burns
patrick at burns-stat.com
+44 (0)20 8525 0696
(home of S Poetry and "A Guide for the Unwilling S User")

oliver wee wrote:

>I have been looking at multiple websites on GARCH and
>have looked at some books and I am getting
>contradictory models given for GARCH.
>If I use the GARCH function to fit my model, I am
>confused as to what the coefficents given refer to.
>For example if I fit a GARCH(1,1) model, GARCH will
>give me three coefficients Ao, Ai, and Bi
>I know Ao refers to the constant of the model.
>But what about Ai and Bi?
>One website I looked at says the model for GARCH is:
>1) S^2t = Ao + Ai S^2 t-1 + Bi E^2 t-1 + Et
>(sigma squared sub t = a sub 0 + a sub 1 sigma squared
>sub t-1 + b sub 1 epsilon squared sub t-1 + epsilon
>sub t)
>while a book I was reading says the general model is
>2) S^2t = Ao + Ai Y^2 t-1 + Bi S^2 t-1
>(sigma squared sub t = a sub 0 + a sub 1 Y squared sub
>t-1 + b sub 1 sigma squared sub t-1).
>where Y refers to the data points of th time series
>S refers to the variance and E refers to the white
>noise component.
>I am very confused by this.
>Also, two other questions regarding GARCH,
>1) How exactly do I forecast future values of my
>fitted GARCH model using R and how do I graph them? 
>predict() won't work since it won't accept the n.ahead
>argument. (Assuming I already have fitted my original
>data set to an ARIMA model and have predicted future
>values using the predict() command).  
>2) This is not about R, but about GARCH in general. I
>just want to check if I understood GARCH correctly. 
>For example, I have already found an ARIMA model to
>fit my original data set. In order for me to find the
>appropriate GARCH model to fit my data set, I have to
>get the acf of the squared values of my original data
>set (assuming the data set is stationary, that is, its
>acf show no significant correlations at all lags, but
>the acf of its squared values is not stationary). Once
>I get the acf of the squared values, I just compare
>this to the acf of arma(p,q) models- similar to how I
>was able to find my fitted ARIMA model? Is this
>correct? Also, once I have found the appropriate GARCH
>model, I can use this model to predict BOTH the future
>values of the data set and its variance? and these 
>future values will be far different than the one given
>my my fitted ARIMA model?
>I am sorry for the abundance of questions and I am
>pretty sure some of these questions sound pretty dumb.
>Its that I'm doing my study of time series mostly
>through self-study and I got really confused about
>Thank you very much for your help.
>R-help at stat.math.ethz.ch mailing list
>PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html

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