Our objective is volatility forecasting, which is core to many risk management problems. We provide theoretical explanations for (i) the empirical stylized fact recognized at least since Taylor (1986) and Ding, Granger, and Engle (1993) that absolute returns show more persistence than squared returns and (ii) the empirical finding reported in recent work by Ghysels, Santa-Clara, and Valkanov (2006) showing that realized absolute values outperform square return-based volatility measures in predicting future increments in quadratic variation. We start from a continuous time stochastic volatility model for asset returns suggested by Barndorff-Nielsen and Shephard (2001) and study the persistence and linear regression properties of various volatility-related processes either observed directly or with sampling error. We also allow for jumps in the asset return processes and investigate their impact on persistence and linear regression. Extensive empirical results complement the theoretical analysis.