1 Department of Marketing and Statistics, Aarhus School of Business, Aarhus BSS, Aarhus University2 Department of Economics and Business Economics, Aarhus BSS, Aarhus University3 Ruhr University of Bochum, Dept. of Probability and Statistics4 Department of Economics and Business Economics, Aarhus BSS, Aarhus University
We provide a set of probabilistic laws for estimating the quadratic variation of continuous semimartingales with realized range-based variance - a statistic that replaces every squared return of realized variance with a normalized squared range. If the entire sample path of the process is available, and under a set of weak conditions, our statistic is consistent and has a mixed Gaussian limit, whose precision is five times greater than that of realized variance. In practice, of course, inference is drawn from discrete data and true ranges are unobserved, leading to downward bias. We solve this problem to get a consistent, mixed normal estimator, irrespective of non-trading effects. This estimator has varying degrees of efficiency over realized variance, depending on how many observations that are used to construct the high-low. The methodology is applied to TAQ data and compared with realized variance. Our findings suggest that the empirical path of quadratic variation is also estimated better with the realized range-based variance.