Volatility measurement with pockets of extreme return persistence

Increasing evidence points towards the episodic emergence of pockets with extreme return persistence. This notion refers to intraday periods of non-trivial duration, for which stock returns are highly positively autocorrelated. Such episodes include, but are not limited to, gradual jumps and prolonged bursts in the drift component. In this paper, we develop a family of integrated volatility estimators, labeled differenced-return volatility (DV) estimators, which provide robustness to these types of Itô semimartingale violations. Specifically, we show that, by using differences in consecutive high-frequency returns, our DV estimators can reduce the non-trivial bias that all commonly-used estimators exhibit during such periods of apparent short-term intraday return predictability. A Monte Carlo study demonstrates the reliability of the newly developed volatility estimators in finite samples. In our empirical volatility forecasting application to S&P 500 index futures and individual equities, our DV-based Heterogeneous Autoregressive (HAR) model performs well relative to existing procedures according to standard out-of-sample MSE and QLIKE criteria.