Symmetrical and Asymmetrical Smooth TransitionAutoregressive-GARCH Model: Estimation and Model Selection

The smooth transition autoregressive generalized autoregressive conditional heteroskedasticity, STAR-GARCH, models are becoming popular in modeling economic and financial time series. The most popular specifications of the transition function are the U-shaped exponential function and the logistic function, which are suitable for modelling economic and financial time series. Estimation of STAR-GARCH is not entirely straightforward, so likelihood functions are then estimated using the numerical method. The convergence of the maximum likelihood estimator for STAR-GARCH models is sensitive to initial values. In this paper, we computed modified maximum likelihood estimators of parameters of STAR-GARCH models and asymptotic distribution of modified maximum likelihood estimators. So that, we can select optimal model based on the Vuong’s test. A set of simulation results also lends strong support to the results presented in the paper.