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This study examines the asymptotic properties of a class of conditionally heteroscedastic location-scale time series models with innovations following a generalized asymmetric Student- t  distribution (ASTD) or an asymmetric exponential power distribution (AEPD). We first show the consistency and asymptotic normality of the conditional maximum likelihood estimator of the model parameters under certain regularity conditions. Then, based on the maximum likelihood estimator, we estimate conditional value-at-risk (VaR) and expected shortfall (ES) by using their closed forms induced from the model. Their performance is finally compared with that of conditional autoregressive VaR and expectile methods. A simulation study and real data analysis are provided as an illustration.

Risk measurement for conditionally heteroscedastic location-scale time series models with ASTD and AEPD innovations