symmetrical and asymmetrical smooth transitionautoregressive-garch model: estimation and model selection

The smooth transition autoregressive generalized autoregressive conditionalheteroskedasticity, star-garch, models are becoming popular in modeling economicand financial time series. the most popular specifications of the transition functionare the u-shaped exponential function and the logistic function, which are suitablefor modelling economic and financial time series. estimation of star-garch is notentirely straightforward, so likelihood functions are then estimated using the numericalmethod. the convergence of the maximum likelihood estimator for star-garchmodels is sensitive to initial values. in this paper, we computed modified maximumlikelihood estimators of parameters of star-garch models and asymptotic distributionof modified maximum likelihood estimators. so that, we can select optimal modelbased on the vuong’s test. a set of simulation results also lends strong support to theresults presented in the paper.