Conditional risk measurement using conditional higher order moments: a dynamic application of the skew t-distribution

This paper presents a parsimonious approach to estimating conditional skewness and kurtosis, as well as conditional variance, in financial log-returns time series. Using a GARCH formulation of the skew t-distribution (Jones and Faddy, 2003), autoregressive relationships are developed for the conditional skewness and conditional kurtosis. A numerical example indicates that allowing for estimates of conditional skewness and kurtosis can improve the estimate of the conditional volatility, as well as provide quantitative indicators of epochs of high risk by identification of increased conditional skewness or kurtosis. The model enables Value-at-Risk to be estimated more conservatively by weakening the requirements of both Normality and independence, thus capturing time-varying risk from more general non-linear financial time series with greater accuracy.