The reason you are getting a discrepancy is because you have not been diligent
in either reading the documentation or the c-code which show the GARCH
recursion:
1. The specification you use is the default one ARMA(1,1)-GARCH(1,1) but you
filter the returns ONLY for a constant.
2. Your code does not include start-up recursion conditions.
Here is the correct way to do it:
#################################
library(rugarch)
data(sp500ret)
calcResiduals<-function(returns, mu){
# pass the correct mu which is estimated jointly in the ML procedure
returns-mu
}
standardGarch<-function(returns, alpha, beta, omega, mu){
residuals<-calcResiduals(returns, mu)
sigmaVect<-rep(0, length(returns))
# recursion initialisation value h0
h0 = mean(residuals^2)
for(i in 1:length(returns)){
if(i==1){
sigmaVect[i]<-h0
} else{
sigmaVect[i]<-omega+alpha*residuals[i-1]^2+beta*sigmaVect[i-1]
}
}
return(sigmaVect)
}
returns<-sp500ret[,1] #leave off the dates for now
# armaOrder=c(0,0) since default is (1,1)
spec<-ugarchspec(mean.model=list(armaOrder=c(0,0)),variance.model=list(model="sGARCH"))
fit<-ugarchfit(spec, sp500ret)
alpha<-coef(fit)["alpha1"]
beta<-coef(fit)["beta1"]
omega<-coef(fit)["omega"]
mu<-coef(fit)["mu"]
vals<-standardGarch(returns,alpha, beta, omega, mu)
# all.equal is the way to compare, NOT visually if you want exact results:
all.equal(as.numeric(sigma(fit)), sqrt(as.numeric(vals)))
################################
-Alexios
On 14 Jul 2014, at 20:02, Tevlin, Dylan <dylan.tev...@kochind.com> wrote:
> Running R 2.1.14 on Windows 7.
>
> My problem is the following:
>
> I'm using the sp500ret data, approximating the parameters using ugarchfit,
> and then calculating the conditional variances "by hand" and plotting on top
> of the 3rd graph from plot.ugarchfit. This task may seem silly but bear with
> me. All the following code is ready to run copy and paste.
>
> The discrepancy I'm finding is consistent over different models, so let's
> just look at a Garch(1,1)
>
> #start code ****************
> library(rugarch)
> data(sp500ret)
>
> #by hand functions
> calcResiduals<-function(returns){
> #returns a list of the returns residuals
>
> #returns :a vector or time series of floats
>
> returns-mean(returns)
> }
>
> standardGarch<-function(returns, alpha, beta, omega){
> #standard garch per rugarch documentation
>
> #returns :a vector or time series of floats
> #alpha :a float, estimation of the alpha parameter
> #beta :a float, estimation of the beta parameter
> #omega :a float, estimation of the omega parameter
>
> residuals<-calcResiduals(returns)
> #now we have our iterative recursive method
> sigmaVect<-rep(0, length(returns)+1)
>
> for(i in 1:length(returns)){
> sigmaVect[i+1]<-omega+alpha*residuals[i]^2+beta*sigmaVect[i]
> }
> sigmaVect
> }
>
> returns<-sp500ret[,1] #leave off the dates for now
>
> spec<-ugarchspec(variance.model=list(model="sGARCH"))
> fit<-ugarchfit(spec, sp500ret)
> fit
> plot(fit) #here press 3 then enter on the console
> #then press 0 then enter to exit the graph menu
>
> #I got the following as estimates for my parameters from ugarchfit
> #these should be changed to the appropriate ones you get in output
> #they should be near the same
> alpha<-.087817
> beta<-.904886
> omega<-.000001
>
> vals<-standardGarch(returns,alpha, beta, omega )
> vals<-vals[2:(length(vals))]
> vals<-as.data.frame(vals)
> rownames(vals)<-rownames(sp500ret) #attach the dates
>
> #yes, the dates are most likely a bit off, that won't matter to much for the
> visual
> #representation though. My issue is a vertical shift difference
>
> lines(sqrt(vals), col="purple")
>
> #plot the by hand calculation on top of the ugarchfit graph.
>
> #end code *******************
>
> On my machine, I see a slight discrepancy between my function's calculation
> of the conditional variances and the ugarchfit calculation. To my
> understanding I implemented the formula used in ugarchfit for sGarch
> correctly, so there should be very little difference in the output.
>
> My first thoughts as to why this difference occurs is some difference in how
> C and R treat numerics and the conversion back and forth (this occurs in
> ugarchfit but not in mine), or possibly some truncation of the parameter
> estimates for display purposes, leading me to use parameter values that are
> slightly off.
>
> Can anyone provide an explanation as to what I am seeing here?
>
> [[alternative HTML version deleted]]
>
> _______________________________________________
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