Bayesian GARCH modeling for return and range

This paper introduces a new generalized autoregressive conditional heteroskedasticity (GARCH) structure, which models the daily return of an asset and the price range simultaneously to describe the time-varying volatility of an asset return. New equations that link the price range to volatility are added to the GARCH and related models based on the density of the range. An algorithm for the Bayesian estimation of the parameters and one-step-ahead forecasting is provided by using the adaptive Markov chain Monte Carlo. The approach is applied to stock index data in Japan and the United Kingdom. The estimation results reveal that the proposed models capture the stylized features of an asset return, such as volatility clustering and asymmetry of the volatility to the return (leverage effect). The downward bias of the range, due to non-trading hours and the market microstructure, is suggested in the estimation. Model comparisons are conducted based on the predictive ability for the volatility, which shows that the new GARCH-type models perform equal to or better than the competing models for the return and the corresponding realized measure of the volatility.