Robustness of score-driven location and scale models to extreme observations: An application to the Chinese stock market

Abstract

Recently, the use of dynamic conditional score (DCS) time series models are suggested in the body of literature on time series econometrics. DCS models are robust to extreme observations because those observations are discounted by the score function that updates each dynamic equation. Examples of the DCS models are the quasi-autoregressive (QAR) model and the Beta-t-EGARCH (exponential generalized autoregressive conditional heteroscedasticity) model, which measure the dynamics of location and scale, respectively, of the dependent variable. Both QAR and Beta-t-EGARCH discount extreme observations according to a smooth form of trimming. Classical dynamic location and scale models (for example, the AR and the GARCH models) are sensitive to extreme observations. Thus, the AR and the GARCH modelsmay provide imprecise estimates of location and scale dynamics. In the application presented in this paper, we use data from the Shanghai Stock Exchange A-Share Index and the Shenzhen Stock Exchange A-Share Index for the period of 5th January 1998 to 29th December 2017. For the corresponding stock index return time series, a relatively high number of extreme values are observed during the sample period. We find that the statistical performance of QAR plus Beta-t-EGARCH is superior to that of AR plus t-GARCH, due to the robustness of QAR plus Beta-t-EGARCH to extreme unexpected returns.