rugarch (version 1.0-16)

VaRDurTest: VaR Duration Test

Description

Implements the VaR Duration Test of Christoffersen and Pelletier.

Usage

VaRDurTest(alpha, actual, VaR, conf.level = 0.95)

Arguments

alpha

The quantile (coverage) used for the VaR.

actual

A numeric vector of the actual (realized) values.

VaR

The numeric vector of VaR.

conf.level

The confidence level at which the Null Hypothesis is evaluated.

Value

• A list with the following items:
• b
  The estimated Weibull parameter which when restricted to the value of 1 results in the Exponential distribution.
• uLL
  The unrestricted Log-Likelihood value.
• rLL
  The restricted Log-Likelihood value.
• LRp
  The Likelihood Ratio Test Statistic.
• H0
  The Null Hypothesis.
• Decision
  The on H0 given the confidence level

Details

The duration of time between VaR violations (no-hits) should ideally be independent and not cluster. Under the null hypothesis of a correctly specified risk model, the no-hit duration should have no memory. Since the only continuous distribution which is memory free is the exponential, the test can conducted on any distribution which embeds the exponential as a restricted case, and a likelihood ratio test then conducted to see whether the restriction holds. Following Christoffersen and Pelletier (2004), the Weibull distribution is used with parameter b=1 representing the case of the exponential. A future release will include the choice of using a bootstrap method to evaluate the p-value, and until then care should be taken when evaluating series of length less than 1000 as a rule of thumb.

References

Christoffersen, P. and Pelletier, D. 2004, Backtesting value-at-risk: A duration-based approach, Journal of Financial Econometrics, 2(1), 84--108.

Examples

data(dji30ret)
spec = ugarchspec(mean.model = list(armaOrder = c(1,1), include.mean = TRUE),
variance.model = list(model = "gjrGARCH"), distribution.model = "sstd")
fit = ugarchfit(spec, data = dji30ret[1:1000, 1, drop = FALSE])
spec2 = spec
setfixed(spec2)<-as.list(coef(fit))
filt = ugarchfilter(spec2, dji30ret[1001:2500, 1, drop = FALSE], n.old = 1000)
actual = dji30ret[1001:2500,1]
# location+scale invariance allows to use [mu + sigma*q(p,0,1,skew,shape)]
VaR = fitted(filt) + sigma(filt)*qdist("sstd", p=0.05, mu = 0, sigma = 1, 
skew  = coef(fit)["skew"], shape=coef(fit)["shape"])
print(VaRDurTest(0.05, actual, VaR))

# Try with the Normal Distribution (it fails)
spec = ugarchspec(mean.model = list(armaOrder = c(1,1), include.mean = TRUE),
variance.model = list(model = "gjrGARCH"), distribution.model = "norm")
fit = ugarchfit(spec, data = dji30ret[1:1000, 1, drop = FALSE])
spec2 = spec
setfixed(spec2)<-as.list(coef(fit))
filt = ugarchfilter(spec2, dji30ret[1001:2500, 1, drop = FALSE], n.old = 1000)
actual = dji30ret[1001:2500,1]
# location+scale invariance allows to use [mu + sigma*q(p,0,1,skew,shape)]
VaR = fitted(filt) + sigma(filt)*qdist("norm", p=0.05, mu = 0, sigma = 1)
print(VaRDurTest(0.05, actual, VaR))