VaRTest: Value at Risk Exceedances Test

In rugarch: Univariate GARCH Models

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.

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.

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.

Author(s)

Alexios Ghalanos

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

## Not run: 
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, as.numeric(actual), as.numeric(VaR)))

## End(Not run)

rugarch documentation built on Sept. 30, 2024, 9:30 a.m.