Quadratic Variation by Markov Chains

Univ. of Aarhus Dept. of Economics Research Paper No. 2009-13

56 Pages Posted: 24 Mar 2009 Last revised: 5 Aug 2009

See all articles by Peter Reinhard Hansen

Peter Reinhard Hansen

University of North Carolina (UNC) at Chapel Hill - Department of Economics; Copenhagen Business School, Finance; Aarhus University - CREATES

Guillaume Horel

Stanford University - Department of Statistics; Merrill Lynch & Co.

Date Written: August 4, 2009

Abstract

We introduce a novel estimator of the quadratic variation that is based on the theory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in principle remove the effects of market microstructure noise in a general framework where little is assumed about the noise. For the practical implementation, we adopt the discrete Markov chain model that is well suited for the analysis of financial high-frequency prices. The Markov chain framework facilitates simple expressions and elegant analytical results. The proposed estimator is consistent with a Gaussian limit distribution and we study its properties in simulations and an empirical application.

Keywords: Markov chain, Filtering Contaminated Semimartingale, Quadratic Variation, Integrated Variance, Realized Variance, High Frequency Data

JEL Classification: C10, C22, C80

Suggested Citation

Hansen, Peter Reinhard and Horel, Guillaume, Quadratic Variation by Markov Chains (August 4, 2009). Univ. of Aarhus Dept. of Economics Research Paper No. 2009-13, Available at SSRN: https://ssrn.com/abstract=1367519 or http://dx.doi.org/10.2139/ssrn.1367519

Peter Reinhard Hansen (Contact Author)

University of North Carolina (UNC) at Chapel Hill - Department of Economics ( email )

Chapel Hill, NC 27599
United States

HOME PAGE: http://https://sites.google.com/site/peterreinhardhansen/

Copenhagen Business School, Finance ( email )

Solbjerg Plads 3
Frederiksberg C, DK - 2000
Denmark

Aarhus University - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Guillaume Horel

Stanford University - Department of Statistics ( email )

Stanford, CA 94305
United States

Merrill Lynch & Co. ( email )

World Financial Center - North Tower
19th Floor
New York, NY 10281-1319
United States

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