BRC-GARCH-X model: the empirical evidence in stock returns

A covariate-driven random coefficient generalized conditional heteroscedasticity (GARCH) time series model with the form of the buffered autoregression (BRC-GARCH-X) for modeling financial time series data is considered. As an extension of the classical two-regime threshold process, the buffered autoregression enjoys a more flexible regime-switching mechanism. Furthermore, the main feature of this model is that the threshold variable for regime-switching is formulated as a weighted average of important auxiliary variables. The estimator for regression parameters is obtained by the quasi-maximum exponential likelihood (QMEL) estimator and the corresponding asymptotic properties are established. Moreover, a mixed portmanteau test is developed for diagnostic checking. And a reasonable method for selecting search ranges for thresholds is also proposed and simulation studies are considered. As an application, we bring attention to some features of of stock returns of SP500 which shows that our model is feasible.