[R-SIG-Finance] Rugarch package using external regressors
Luigi Maria Briglia
luigimaria.briglia at gmail.com
Mon Aug 29 17:28:06 CEST 2016
I’m using the rugarch package and I’m having troubles understanding how the external.regressors work.
For example I would expect that fitting a time series with gjr-garch(1,1) should give the same results as fitting the same time series with the plain vanilla garch(1,1) augmented with S_(t-1)*eps_(t-1)^2 as an external regressor.
However I'm not getting the same results.
Specifically this is the code I'm running:
rm(list = ls()) # empty memory
library(rugarch)
library(xts)
data(sp500ret)
spx <- xts(sp500ret, as.Date(rownames(sp500ret)))
t = length(spx)
# assuming mu = 0; r_t = eps_t
s = rep(0,t)
for(i in 1:t){
if(spx[i]<0){s[i]=1}
}
# eps.neg represents the leverage effect regressor
eps.neg <- xts(spx*s, as.Date(rownames(sp500ret)))
colnames(eps.neg)<-"eps.neg"
# lag eps.neg
eps.neg.lag = lag(eps.neg,1)
inputs<-na.omit(cbind(spx, eps.neg.lag, join="left"))
# gjrgarch(1,1)
gjr.spec <- ugarchspec(variance.model = list(model='gjrGARCH', garchOrder=c(1,1),
external.regressors = NULL, variance.targeting = T),
mean.model = list(armaOrder=c(0,0)),fixed.pars=list(mu = 0))
gjr.fit <- ugarchfit(spec=gjr.spec, data=inputs[,1],
solver.control=list(trace = 1))
# garch(1,1) augmented with inputs[,2]
aug.s.spec <- ugarchspec(variance.model = list(model='sGARCH', garchOrder=c(1,1),
external.regressors = inputs[,2]^2, variance.targeting = T),
mean.model = list(armaOrder=c(0,0)),fixed.pars=list(mu = 0))
aug.s.fit <- ugarchfit(spec=aug.s.spec, data=inputs[,1],
solver.control=list(trace = 1))
#results
gjr.fit
aug.s.fit
However these are the results:
GJR-GARCH(1,1)
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
mu 0.000000 NA NA NA
alpha1 0.007933 0.000184 43.139 0
beta1 0.909048 0.000008 117316.512 0
gamma1 0.139258 0.004006 34.764 0
omega 0.000002 NA NA NA
Augmented-Garch(1,1)
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
mu 0.000000 NA NA NA
alpha1 0.085378 0.002123 4.0223e+01 0.00000
beta1 0.904696 0.000001 1.0116e+06 0.00000
vxreg1 0.000000 0.000060 1.6700e-04 0.99987
omega 0.000001 NA NA NA
clearly the two fits are not equivalent. Is there something I’m missing about the external.regressors?
[[alternative HTML version deleted]]
More information about the R-SIG-Finance
mailing list