Volatility Forecasting Using Quasi-Score-Driven Models with an Application to the Coronavirus Pandemic Period

We study the statistical and volatility forecasting performances of the recent quasi-score-driven EGARCH (exponential generalized autoregressive conditional heteroscedasticity) models. We compare the quasi-score-driven EGARCH models with GARCH, asymmetric power ARCH (A-PARCH), and all relevant score-driven EGARCH models of the literature. For score-driven and quasi-score-driven EGARCH, we use the following seven score-driven probability distributions: Student’s t-distribution; general error distribution (GED); generalized t-distribution (Gen-t); skewed generalized t-distribution (Skew-Gen-t); exponential generalized beta distribution of the second kind (EGB2); normal-inverse Gaussian distribution (NIG); Meixner distribution (MXN). We use all combinations of those distributions for (i) the probability distribution of the dependent variable, and (ii) the probability distribution which defines the quasi-score function updating term of the quasi-score-driven filters. We use daily data for the Standard & Poor’s 500 (S&P 500) index. We find that both in-sample and out-of-sample, quasi-score-driven EGARCH is superior to GARCH, A-PARCH, and score-driven EGARCH. We report in-sample results for the period of January 2000 to December 2020, providing evidence in favor of the quasi-score-driven EGARCH model for the last two decades. We report out-of-sample volatility forecasting results for a period within the coronavirus disease 2019 (COVID-19) pandemic, providing evidence in favor of the quasi-score-driven EGARCH model for a crisis period.