[R-SIG-Finance] Rugarch package using external regressors

[alexios galanos]

Yes, you are missing good default bounds for the external regressors.
Try:
setbounds(aug.s.spec)<-list("vxreg1"=c(-1, 1))

This gives me the same results.

Alexios

On 29/08/2016 18:28, Luigi Maria Briglia wrote:
> 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?
>
>
>
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