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 …ltering contaminated semimartingales. Speci…cally, we show that …ltering can in principle remove the e¤ects 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 …nancial 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
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