| ESTest {rugarch} | R Documentation |
Implements the Expected Shortfall Test of McNeil and Frey.
ESTest(alpha = 0.05, actual, ES, VaR, conf.level = 0.95, boot = FALSE, n.boot = 1000)
alpha |
The quantile (coverage) used for the VaR. |
actual |
A numeric vector of the actual (realized) values. |
ES |
The numeric vector of the Expected Shortfall (ES). |
VaR |
The numeric vector of VaR. |
conf.level |
The confidence level at which the Null Hypothesis is evaluated. |
boot |
Whether to bootstrap the test. |
n.boot |
Number of bootstrap replications to use. |
The Null hypothesis is that the excess conditional shortfall (excess of the actual series when VaR is violated), is i.i.d. and has zero mean. The test is a one sided t-test against the alternative that the excess shortfall has mean greater than zero and thus that the conditional shortfall is systematically underestimated. Using the bootstrap to obtain the p-value should alleviate any bias with respect to assumptions about the underlying distribution of the excess shortfall.
A list with the following items:
expected.exceed |
The expected number of exceedances (length actual x coverage). |
actual.exceed |
The actual number of exceedances. |
H1 |
The Alternative Hypothesis of the one sided test (see details). |
boot.p.value |
The bootstrapped p-value (if used). |
p.value |
The p-value. |
Decision |
The one-sided test Decision on H0 given the confidence level and p-value (not the bootstrapped). |
Alexios Ghalanos
McNeil, A.J. and Frey, R. and Embrechts, P. (2000), Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach, Journal of Empirical Finance,7, 271–300.
## 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"])
# calculate ES
f = function(x) qdist("sstd", p=x, mu = 0, sigma = 1,
skew = coef(fit)["skew"], shape=coef(fit)["shape"])
ES = fitted(filt) + sigma(filt)*integrate(f, 0, 0.05)$value/0.05
print(ESTest(0.05, actual, ES, VaR, boot = TRUE))
## End(Not run)