  This paper provides an insight to the time-varying dynamics of the shape of
the distribution of financial return series by proposing an exponential
weighted moving average model that jointly estimates volatility, skewness and
kurtosis over time using a modified form of the Gram-Charlier density in which
skewness and kurtosis appear directly in the functional form of this density.
In this setting VaR can be described as a function of the time-varying higher
moments by applying the Cornish-Fisher expansion series of the first four
moments. An evaluation of the predictive performance of the proposed model in
the estimation of 1-day and 10-day VaR forecasts is performed in comparison
with the historical simulation, filtered historical simulation and GARCH model.
The adequacy of the VaR forecasts is evaluated under the unconditional,
independence and conditional likelihood ratio tests as well as Basel II
regulatory tests. The results presented have significant implications for risk
management, trading and hedging activities as well as in the pricing of equity
derivatives.
