The Contribution of Intraday Jumps to Forecasting the Density of Returns

Recent contributions highlight the importance of intraday jumps in forecasting realized volatility at horizons up to one month. We extend the methodology developed in Maheu and McCurdy (2011) to exploit the information content of intraday data in forecasting the density of returns. Considering both intra-week periodicity and signed jumps, we estimate two variants of a bivariate model of returns and volatilities where the jump component is independently modeled. Our empirical results for four futures series (S&P 500, U.S. 10-year Treasury, USD/CAD exchange rate and WTI crude oil) highlight the importance of considering the continuous/jump decomposition of volatility for the purpose of density forecasting. Specifically, we show that models considering jumps apart from the continuous component consistently deliver better density forecasts for horizons up to one month and a half and, in two cases out of four, for horizons up to three months