A multiple indicators model for volatility using intra-daily data

Many ways exist to measure and model financial asset volatility. In principle, as the frequency of the data increases, the quality of forecasts should improve. Yet, there is no consensus about a “true” or “best” measure of volatility. In this paper we propose to jointly consider absolute daily returns, daily high–low range and daily realized volatility to develop a forecasting model based on their conditional dynamics. As all are non-negative series, we develop a multiplicative error model that is consistent and asymptotically normal under a wide range of specifications for the error density function. The estimation results show significant interactions between the indicators. We also show that one-month-ahead forecasts match well (both in and out of sample) the market-based volatility measure provided by the VIX index as recently redefined by the CBOE.