Many recent modelling advances in finance topics ranging from the pricing of volatility-based derivative products to asset management are predicated on the importance of jumps, or discontinuous movements in asset returns. In light of this, a number of recent papers have addressed volatility predictability, some from the perspective of the usefulness of jumps in forecasting volatility. Key papers in this area include Andersen, Bollerslev, Diebold and Labys (2003), Corsi (2004), Andersen, Bollerslev and Diebold (2007), Corsi, Pirino and Reno (2008), Barndorff, Kinnebrock, and Shephard (2010), Patton and Shephard (2011), and the references cited therein. In this paper, we review the extant literature and then present new empirical evidence on the predictive content of realized measures of jump power variations (including upside and downside risk, jump asymmetry, and truncated jump variables), constructed using instantaneous returns, i.e., |r_{t}|^{q}, 0≤q≤6, in the spirit of Ding, Granger and Engle (1993) and Ding and Granger (1996). Our prediction experiments use high frequency price returns constructed using S&P500 futures data as well as stocks in the Dow 30; and our empirical implementation involves estimating linear and nonlinear heterogeneous autoregressive realized volatility (HAR-RV) type models. We find that past "large" jump power variations help less in the prediction of future realized volatility, than past "small" jump power variations. Additionally, we find evidence that past realized signed jump power variations, which have not previously been examined in this literature, are strongly correlated with future volatility, and that past downside jump variations matter in prediction. Finally, incorporation of downside and upside jump power variations does improve predictability, albeit to a limited extent.
