[R-SIG-Finance] rugarch package / VaR Duration Test / Size Property

[TobiB]

Hi,

I want to assess the size properties of the duration based VaR backtest of
Christoffersen and Pelletier (2004) by simulating i.i.d. Bernoulli variables
and using the function VaRDurTest() of the rugarch package. I am aware that
the size property is bad when evaluating small series, but even for a series
length of e.g. 10,000 I do not achieve the accurate significance level.
Furthermore, the size property become worse if the series length increases. 
Has anybody an idea, what I have done wrong?

 I use the following code for the evaluation:

library(rugarch)
VaR.quantile = 0.05	#VaR quantile
fc.period = 10000	        #Length Forecasting-Period
n.sim = 10000		#Number of simulations

DurTest.p = rep(0,n.sim)
test=0
outlier=0
i=0

while (test<n.sim)
{
	return.vec = (-1)*rbinom(fc.period,1,VaR.quantile)     #Return vector 
	var <- rep(-0.5,fc.period)                                                 
#VaR vector

	if (sum(return.vec)< -1)                                                     
#Exclude ouliers (sum of VaR violations<2)
	{	
		test = test+1
		DurTest.p[test] = VaRDurTest(alpha = VaR.quantile, actual = return.vec,
VaR = var, conf.level = 0.95)$LRp
	}	else {outlier = outlier+1}
	i=i+1
	print(c(i,test,outlier))	
}

rbind(
res.DurTest.001 = length(which(DurTest.p<=0.001))/test,
res.DurTest.01 = length(which(DurTest.p<=0.01))/test,
res.DurTest.05 = length(which(DurTest.p<=0.05))/test,
res.DurTest.10 = length(which(DurTest.p<=0.10))/test)
#


The application of this code leads to the following results:

res.DurTest.001 0.0715   # 0.1% Level
res.DurTest.01  0.2437    # 1% Level
res.DurTest.05  0.4953    # 5% Level
res.DurTest.10  0.6274   # 10% Level

Instead of using the code

	return.vec = (-1)*rbinom(fc.period,1,VaR.quantile)     #Return vector 
	var <- rep(-0.5,fc.period)                                                 
#VaR vector

to simulate an i.i.d Bernoulli distributed hit sequence, I also tried

	return.vec = rnorm(fc.period,0,0.1)
	var = rep(qnorm(VaR.quantile,0,0.1),fc.period)

However, the results are the same.

Thanks in advance.
TB




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