rugarch (version 1.0-16)

VaRTest: Value at Risk Exceedances Test

Description

Implements the unconditional and conditional coverage Value at Risk Exceedances Test.

Usage

VaRTest(alpha = 0.05, 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:
• expected.exceed
  The expected number of exceedances (length actual x coverage).
• actual.exceed
  The actual number of exceedances.
• uc.H0
  The unconditional coverage test Null Hypothesis.
• uc.LRstat
  The unconditional coverage test Likelihood Ratio statistic.
• uc.critical
  The unconditional coverage test critical value.
• uc.LRp
  The unconditional coverage test p-value.
• uc.H0
  The unconditional coverage test Null Hypothesis.
• uc.Decision
  The unconditional coverage test Decision on H0 given the confidence level.
• cc.H0
  The conditional coverage test Null Hypothesis.
• cc.LRstat
  The conditional coverage test Likelihood Ratio statistic.
• cc.critical
  The conditional coverage test critical value.
• cc.LRp
  The conditional coverage test p-value.
• cc.H0
  The conditional coverage test Null Hypothesis.
• cc.Decision
  The conditional coverage test Decision on H0 given the confidence level.

Details

The test implements both the unconditional (Kupiec) and conditional(Christoffersen) coverage tests for the correct number of exceedances. See the references for further details.

References

Christoffersen, P. (1998), Evaluating Interval Forecasts, International Economic Review, 39, 841--862. Christoffersen, P., Hahn,J. and Inoue, A. (2001), Testing and Comparing Value-at-Risk Measures, Journal of Empirical Finance, 8, 325--342.

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(VaRTest(0.05, actual, VaR))