Theoretical and practical interest in regime switching models has increased rapidly in recent years. Given the substantial research activity in analysing time-varying GARCH volatility, it is useful to investigate regime switching models with GARCH errors. A popular specification of non-linear time series model is Smooth Transition Autoregressive - GARCH (STAR-GARCH). However, little is known about the structural properties of STAR-GARCH models and the finite sample properties of the estimators of STAR and STAR-GARCH models. This paper examines maximum likelihood estimation of these models through numerical simulation, with reference to recent theoretical advances. The finite sample statistical properties of STAR-GARCH models, and the effects of correct and incorrect specification of the conditional mean and/or the transition function of both STAR and STAR-GARCH models, are examined.