The study aims to extend the GARCH type volatility models to their nonlinear TAR (Tong, 1990) and STAR-based (Terasvirta, 1994) counter parts where both the conditional mean and the conditional variance processes follow TAR and STAR nonlinearity. The paper further investigates the models under their fractional integration and asymmetric power variants. The STAR-based models are LSTAR-LST-GARCH, LSTAR-LST-FIGARCH, LSTAR-LST-FIPGARCH and LSTAR-LST-FIAPGARCH models, which may be easily applied to model and forecast various financial time series. In the empirical section, an application is provided to model the daily returns in WTI crude oil prices considering the regime shifts the crude oil prices were subject to during history. Models are evaluated in terms of their out-of-sample forecasting capabilities with equal forecast accuracy tests and also in terms of various error criteria. The results suggest that volatility clustering, asymmetry and nonlinearity characteristics are modeled more efficiently as compared to their single regime variants, such as the GARCH, FIGARCH and FIAPGARCH models. Further, the out-of-sample results suggest that the LSTAR-LST-FIAPGARCH model provides the best forecasting accuracy in terms of RMSE and MSE error criteria.