Predictive inference for integrated volatility

In recent years, numerous volatility-based derivative products have been engineered. This has led to interest in constructing conditional predictive densities and confidence intervals for integrated volatility. In this paper, we propose nonparametric estimators of the aforementioned quantities, based on model free volatility estimators. We establish consistency and asymptotic normality for the feasible estimators and study their finite sample properties through a Monte Carlo experiment. Finally, using data from the New York Stock Exchange, we provide an empirical application to volatility directional predictability.