Forecasting the One-period-ahead Volatility of the International Stock Indices: GARCH Model vs. GM(1,1)-GARCH Model

Abstract

In this paper, we propose a hybrid model, denoted as GM(1,1)-GARCH, that combines the grey forecasting model with the GARCH model to enhance the one-step-ahead variance forecasting ability as compared to the traditional GARCH model. Due to the trite underlying volatility process is not observed, a range-based measure of ex post volatility is employed as a proxy for the unobservable volatility process in evaluating the forecasting ability. Four international stock indices are illustrated to carry out the empirical investigation, and out-of-sample periods are divided into all data, up-trending and down-trending ones. The results indicate that the one-step-ahead variance forecasts produced by GM(1,1)-GARCH(1,1) model have higher R^2 and lower MAE, RMSE and MAPE for most cases as compared to GARCH(1,1) model. As a whole, this results provides the evidences that the hybrid GM(1,1)-GARCH model could enhance one-period-ahead volatility forecasting ability of the traditional GARCH model.