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Measuring and forecasting volatility of asset returns is very important for asset trading and risk management. There are various forms of volatility estimates, including implied volatility, realized volatility and volatility assumed under stochastic volatility models and GARCH models. Research has shown that these different methods are closely related but have different perspectives, strengths and weaknesses. In order to exploit their connections and take advantage of their different strengths, in this paper, we propose to jointly model them with a vector fractionally integrated autoregressive and moving average (VARFIMA) model. The model is also used for forecasting purpose. In addition, we investigate the impacts of the two realized volatility estimators obtained from intra-daily high frequency data on the forecasts of return volatility. Our methods are applied to five individual stocks and forecasting performances are compared with those from a GARCH(1,1) model and a basic stochastic volatility (SV) model and their extended versions. The proposed VARFIMA model outperforms other volatility forecasting models in this study. Our results show that including the two different realized volatility estimators obtained from the intra-daily high frequency data in the VARFIMA model imposes significant impacts on the forecasting precision for return volatility.

Forecasting return volatility in the presence of microstructure noise