Asymptotic Theory of Range-Based Multipower Variation

Journal of Financial Econometrics, Forthcoming

53 Pages Posted: 20 Apr 2006 Last revised: 26 Nov 2011

See all articles by Kim Christensen

Kim Christensen

Aarhus University - CREATES

Mark Podolskij

University of Heidelberg - Institute of Applied Mathematics

Date Written: October 2011


In this paper, we present a realised range-based multipower variation theory, which can be used to estimate return variation and draw jump-robust inference about the diffusive volatility component, when a high-frequency record of asset prices is available. The standard range-statistic -- routinely used in financial economics to estimate the variance of securities prices -- is shown to be biased when the price process contains jumps. We outline how the new theory can be applied to remove this bias by constructing a hybrid range-based estimator. Our asymptotic theory also reveals that when high-frequency data are sparsely sampled, as is often done in practice due to the presence of microstructure noise, the range-based multipower variations can produce significant efficiency gains over comparable subsampled return-based estimators. The analysis is supported by a simulation study and we illustrate the practical use of our framework on some recent TAQ equity data.

Keywords: High-frequency data, Integrated variance, Realised multipower variation, Realised range-based multipower variation, Quadratic variation

JEL Classification: C10, C80

Suggested Citation

Christensen, Kim and Podolskij, Mark, Asymptotic Theory of Range-Based Multipower Variation (October 2011). Journal of Financial Econometrics, Forthcoming. Available at SSRN:

Kim Christensen (Contact Author)

Aarhus University - CREATES ( email )

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

Mark Podolskij

University of Heidelberg - Institute of Applied Mathematics ( email )

Grabengasse 1
Heidelberg, 69117
00496221546276 (Phone)

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