In recent decades, many studies have focused on the forecasting of volatility. The GARCH model provides the heteroskedasticity of the asset returns. But estimating the volatility can be difficult, because volatility is not observable. Chou(2005) proposed CARR (Conditional Autoregressive Range) model to explain the time-varying of range. In this study, We use CARR model by using TAIEX index data for 1999-2011,to compare different distribution (exponential, Weibull and Gamma distribution). And combine the CARR model and GARCH model, to compare the out-of-sample forecasts of Range-based GARCH and Return-based GARCH. We find the Gamma distribution is the best of those assumptions. And GARCH-CARR model provides the better prediction of volatility.
