Volatility Estimation and Forecasts Based on Price Durations

We investigate price duration variance estimators that have long been neglected in the literature. We show i) how price duration estimators can be used for the estimation and forecasting of the integrated variance of an underlying semi-martingale price process and ii) how they are affected by a) important market microstructure noise effects such as the bid/ask spread, irregularly spaced observations in discrete time and discrete price levels, as well as b) large price jumps. We develop i) simple-to-construct non-parametric estimators and ii) parametric price duration estimators using autoregressive conditional duration specifications. We derive the asymptotic properties of our non-parametric estimator with and without the presence of some of the microstructure noise we consider. We provide guidance about how our estimators can best be implemented in practice by appropriately selecting a threshold parameter that defines a price duration event, or by averaging over a range of non-parametric duration estimators. We provide simulation and forecasting evidence that price duration estimators can extract relevant information from high-frequency data better and produce more accurate forecasts than competing realized volatility and option-implied variance estimators, when considered in isolation or as part of a forecasting combination setting