Hi there

I'd like to ask for help regarding the correct way to write an
ARMA(0,0)-GJR-GARCH(1,1) model from "ugarchspec/ugarchfit" output.

To make the question reproduceable, I am using Tsay's lecture:
http://faculty.chicagobooth.edu/ruey.tsay/teaching/bs41202/sp2011/lec5-11.pdf
and accompanying data:
http://faculty.chicagobooth.edu/ruey.tsay/teaching/bs41202/sp2011/m-ibm2609.txt

Reading in and transforming the data:

library(fGarch)
library(rugarch)

da=read.table("C:/Users/Gareth/Desktop/Masters/Code/RCode/Tsay
workings/m-ibm2609.txt",header=T,sep="",row.names=1)
ibmlog=log(da$ibm+1)

1. The initial (and logical) attempt is as follows:

gjrgarch.spec5<-ugarchspec(variance.model=list(model="gjrGARCH",garchOrder=c(1,1)),
                           mean.model=list(armaOrder=c(0,0),include.mean=T,
                           archm=F,arfima=F),distribution.model="std")
mod.fit.gjrgarch5<-ugarchfit(spec=gjrgarch.spec5,data=ibmlog)
show(mod.fit.gjrgarch5)

Output:
               Estimate  Std. Error  t value Pr(>|t|)
mu         0.012048    0.001872   6.4374 0.000000
omega    0.000399    0.000146   2.7386 0.006170
alpha1    0.063089    0.027832   2.2668 0.023406
beta1      0.807147    0.048368  16.6875 0.000000
gamma1  0.093631    0.049654   1.8857 0.059338
shape      6.672720    1.327638   5.0260 0.000001

Is this the output to use in writing up a GJR-GARCH(1,1) model, with
Student t-distr. residuals?

2. The second attempt follows (per information in the"ugarchspec" vignette):

gjrgch.spec5<-ugarchspec(variance.model=list(model="fGARCH",garchOrder=c(1,1),

submodel="GJRGARCH"),mean.model=list(armaOrder=c(0,0),include.mean=T,
                archm=F,arfima=F),distribution.model="std")
mod.fit.gjrgch5<-ugarchfit(spec=gjrgch.spec5,data=ibmlog)
show(mod.fit.gjrgch5)

This 2nd attempt output, below, matches Tsay's notes (p.9), but specifies
an APARCH model format (per Tsay's notes, p.5):
             Estimate  Std. Error  t value Pr(>|t|)
mu        0.012048    0.001872   6.4377 0.000000
omega   0.000399    0.000146   2.7384 0.006173
alpha1   0.104681    0.027973   3.7422 0.000182
beta1    0.807113    0.048381  16.6824 0.000000
eta11    0.223600    0.115947   1.9285 0.053796
shape   6.672451    1.327378   5.0268 0.000000

So, according to Tsay, the output here allows me to write up an APARCH
model, although I specify the submodel="GJRGARCH".
My goal is to use estimates in GJR-GARCH model format.

3. Tsay's actual code that gets almost the identical output as (2) above is:

m5=garchFit(~aparch(1,1),data=ibmlog,trace=F,delta=2,leverage=T,include.delta=F,cond.dist="std")
summary(m5)

        mu       omega         alpha1         gamma1       beta1
shape
0.01204765  0.00039898  0.10467694  0.22366008  0.80711061  6.67328733


Does the output from (1) correctly specify the GJR-GARCH model estimates
(p.5 in Tsay's notes), in the context of this example?
i.e. can I put the estimates from (1) into the GJR-GARCH model format?

Many thanks
Gareth McEwan


NOTE: the APARCH model specifies the GJR-GARCH when "delta=2" (and, I
assume, when "leverage=T"). I am just not sure how to use these estimates
when writing out the GJR-GARCH model.

	[[alternative HTML version deleted]]

