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

1 | ```
VaRTest(alpha = 0.05, actual, VaR, conf.level = 0.95)
``` |

`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. |

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

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. |

Alexios Ghalanos

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
## 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)
``` |

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