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
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: Suggested Citation
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