Realized Range-Based Estimation of Integrated Variance

40 Pages Posted: 9 Jun 2005 Last revised: 6 Sep 2010

See all articles by Kim Christensen

Kim Christensen

Aarhus University - CREATES

Mark Podolskij

University of Heidelberg - Institute of Applied Mathematics

Date Written: June 4, 2006

Abstract

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.

Keywords: Central Limit Theorem, Continuous Semimartingales, Integrated Variance, Realized Range-Based Variance, Realized Variance

JEL Classification: C10, C22, C80

Suggested Citation

Christensen, Kim and Podolskij, Mark, Realized Range-Based Estimation of Integrated Variance (June 4, 2006). Journal of Econometrics, Vol. 141, No. 2, 2007. Available at SSRN: https://ssrn.com/abstract=740288

Kim Christensen (Contact Author)

Aarhus University - CREATES ( email )

Department of Economics and Business Economics
Fuglesangs Allé 4
Aarhus V, 8210
Denmark

Mark Podolskij

University of Heidelberg - Institute of Applied Mathematics ( email )

Grabengasse 1
Heidelberg, 69117
Germany
00496221546276 (Phone)

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