# How Large a Difference Can Be Expected Between Standard GARCH and Asymmetric GARCH Volatility Forecasts?

I have been using various GARCH-based models to forecast volatility for various North American equities using historical daily data as inputs.

Asymmetric GARCH models are often cited as a modification of the basic GARCH model to account for the 'leverage effect' i.e. volatility tends to increase more after a negative return than a similarly sized positive return.

What kind of a difference would you expect to see between a standard GARCH and an asymmetric GARCH forecast for a broad-based equity index like the S&P 500 or the NASDAQ-100?

There is nothing particularly special about these two indices, but I think it is helpful to give something concrete to focus the discussion, as I am sure the effect would be different depending on the equities used.

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Generally, by not allowing for assymetry, you expect the effect of shocks to last longers: i.e. the half-life increases (the half life is the number of units of time, after a 1 S.D. shock to $\epsilon_{t-1}$ for $\hat{\sigma}t|I{t-1}$ to come back to the its unconditional value.)

Here is a code snipped that downloads stock data, fits (e)Garch and computes half lifes, in R:

install.packages("rgarch",repos="http://R-Forge.R-project.org")
install.packages("fGarch")
install.packages("fImport")
library(rgarch)
library(fImport)
library(fGarch)
d1<-yahooSeries(symbols="ibm",nDaysBack=1000,frequency=c("daily"))[,4]
dprice1<-diff(log(as.numeric(d1[length(d1):1])))
spec1<-ugarchspec(variance.model=list(model="eGARCH",garchOrder=c(1,1)),mean.model=list(armaOrder=c(0,0),include.mean=T))
spec2<-ugarchspec(variance.model=list(model="fGARCH",submodel="GARCH",garchOrder=c(1,1)),mean.model=list(armaOrder=c(0,0),include.mean=T))
fit1<-ugarchfit(data=dprice1,spec=spec1)
fit2<-ugarchfit(data=dprice1,spec=spec2)
halflife(fit1)
halflife(fit2)


The reason for this is that generally speaking, negative spells tend to be more persistent. If you don't control for this, you will generally bias the $\beta$ (i.e. persistance parameters) downwards.

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there is a significant difference and there a couple of published papers to that effect

1. Comparative Performance of Volatility Models for Oil Price

International Journal of Energy Economics and Policy Vol. 2, No. 3, 2012, pp.167-183 ISSN: 2146-4553 www.econjournals.com

and many more

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