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]] _______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-sig-finance -- Subscriber-posting only. If you want to post, subscribe first. -- Also note that this is not the r-help list where general R questions should go.
