tstests (version 1.0.0)

var_cp_test: Value at Risk CP Test

Description

The value at risk coverage and duration tests of Kupiec (1995) and Christoffersen and Pelletier (1998,2004).

Usage

var_cp_test(actual, forecast, alpha, ...)

Value

An object of class “tstest.var_cp” which has a print and as_flextable method.

Arguments

actual

a series representing the actual value of the series in the out of sample period.

forecast

the forecast values of the series at the quantile given by alpha (the forecast value at risk).

alpha

the quantile level used to calculate the forecast value at risk.

...

not currently used.

Details

The unconditional (Kupiec 1995) and conditional (Christoffersen and Pelletier 1998) coverage tests evaluate the correctness and independence of value at risk violations (failures), individually and jointly. Correctness is measured in terms of the expected and actual violations of value at risk for a given quantile and data size, whilst independence checks the clustering of violations with past violations, which is key in determining whether a model can accurately capture the higher order dynamics of a series. The duration of time between value ar risk 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.

References

Kupiec1995tstests

Christoffersen1998tstests

Christoffersen2004tstests

Examples

library(tsdistributions)
data("garch_forecast")
q <- qdist("jsu", p = 0.05, mu = garch_forecast$forecast, sigma = garch_forecast$sigma,
skew = garch_forecast$skew, shape = garch_forecast$shape)
var_cp_test(actual = garch_forecast$actual, forecast = q, alpha = 0.05)