This paper compares a number of different extreme value models for determining the value at risk (VaR) of three LIFFE futures contracts. A semi-nonparametric approach is also proposed, where the tail events are modeled using the generalised Pareto distribution, and normal market conditions are captured by the empirical distribution function. The value at risk estimates from this approach are compared with those of standard nonparametric extreme value tail estimation approaches, with a small sample bias-corrected extreme value approach, and with those calculated from bootstrapping the unconditional density and bootstrapping from a GARCH(1,1) model. The results indicate that, for a holdout sample, the proposed semi-nonparametric extreme value approach yields superior results to other methods, but the small sample tail index technique is also accurate. D
This paper investigates the statistical properties of the trispectrum. The trispectrum is the Fourier transform of the fourth-order joint lagged cumulant of a zero-mean stationary random time series. A complete representation of the principal domain of the trispectrum derived from its inherent symmetries is detailed. The large sample variance for a consistent estimator of the trispectrum is presented and used in the development of the fourth-order generalizations of the bispectrum-based Hinich tests of Gaussianity and linearity. A test for stationarity is developed using an amended version of the trispectrum-based test of Gaussianity. An arithmetic frame-averaging procedure is used to compute consistent trispectral estimates for a zero-mean bandlimited real-valued stationary random process. The trispectral-based tests are applied to time series of ship noise recorded by a sonobouy in the Eastern Atlantic Ocean.
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