Forecasting VaR and ES using dynamic conditional score models and skew Student distribution

Dynamic conditional score (DCS) model is a new type of observation-driven model based on the score function. Based on time-varying scale, Harvey (2013) proposed univariate DCS models with skew Student distribution. We redescribe these models based on log-variance and extend them to models based on variance. In the modeling process, calculating score of the distribution is a key part. When selecting scale or variance to calculate the score, two subclasses of DCS models with skew Student distribution are derived. We study them separately in detail, and the models with leverage have been presented too. For estimating one-day-ahead VaR and ES, we combine these models with AR(1) into new ones. By backtesting their performance for four international stock indices, we find that all these AR-DCS models perform well on forcasting VaR and ES at the confidence levels 95%, 99% and 99.5%.