Dynamic conditional score models of degrees of freedom: filtering with score-driven heavy tails

This article extends the quasi-autoregressive (QAR) plus Beta-t-EGARCH (exponential generalized autoregressive conditional heteroscedasticity) dynamic conditional score (DCS) model. For the new DCS model, the degrees of freedom parameter is time varying and tail thickness of the error term is updated by the conditional score. We compare the performance of QAR plus Beta-t-EGARCH with constant degrees of freedom (benchmark model) and QAR plus Beta-t-EGARCH with time-varying degrees of freedom (extended model). We use data from the Standard and Poor’s 500 (S&P 500) index, and a random sample of its 150 components that are from different industries of the United States (US) economy. For the S&P 500, all likelihood-based model selection criteria support the extended model, which identifies extreme events with significant impact on the US stock market. We find that for 59% of the 150 firms, the extended model has a superior statistical performance. The results suggest that the extended model is superior for those industries, which produce products that people usually are unwilling to cut out of their budgets, regardless of their financial situation. We perform an application to compare the density forecast performance of both DCS models. We perform an application to Monte Carlo value-at-risk for both DCS models.