Mixed exponential power asymmetric conditional heteroskedasticity

To match the stylized facts of high frequency financial time series precisely andparsimoniously, this paper presents a finite mixture of conditional exponential powerdistributions where each component exhibits asymmetric conditional heteroskedasticity. Weprovide stationarity conditions and unconditional moments to the fourth order. We apply thisnew class to Dow Jones index returns. We find that a two-component mixed exponentialpower distribution dominates mixed normal distributions with more components, and moreparameters, both in-sample and out-of-sample. In contrast to mixed normal distributions, allthe conditional variance processes become stationary. This happens because the mixedexponential power distribution allows for component-specific shape parameters so that it canbetter capture the tail behaviour. Therefore, the more general new class has attractive featuresover mixed normal distributions in our application: Less components are necessary and theconditional variances in the components are stationary processes. Results on NASDAQ indexreturns are similar.