Innovation of the Component GARCH Model: Simulation Evidence and Application on the Chinese Stock Market

The component GARCH model (CGARCH) was among the first attempts to split the conditional variance into a permanent and transitory component. With the application to economic and finance data, it helps investigate the long- and short-run movements of volatility affecting securities. Like all GARCH-type models, the innovation series of the CGARCH are usually assumed to follow a Normal distribution, which cannot accommodate fat-tailed properties commonly present in empirical data. The resulting estimates are not efficient when a Normal assumption is employed. In this paper, we consider the tempered stable distribution, which has the attractive stability under aggregation property missed in other popular fat-tailed distributions such as Student's t-distribution and General Error Distribution (GED). Through systematically designed simulation studies, our results demonstrate that a CGARCH model with tempered stable distribution uniformly outperforms those with Normal, Student's t-distribution and GED. Our empirical study on the Shanghai Stock Exchange index also leads to the same conclusions. Therefore, we argue that the CGARCH model with tempered stable distribution could be widely used to model economic and financial data in general contexts, focusing on both the long- and short-run volatility behaviours.