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Estimating the Quadratic Covariation Matrix from Noisy Observations: Local Method of Moments and Efficiency

39 Pages Posted: 26 Aug 2013  

Markus Bibinger

University of Mannheim

Nikolaus Hautsch

University of Vienna - Department of Statistics and Operations Research; Center for Financial Studies (CFS)

Peter Malec

University of Cambridge - Faculty of Economics

Markus Reiss

Humboldt University of Berlin

Date Written: August 25, 2013

Abstract

An efficient estimator is constructed for the quadratic covariation or integrated covolatility matrix of a multivariate continuous martingale based on noisy and non-synchronous observations under high-frequency asymptotics. Our approach relies on an asymptotically equivalent continuous-time observation model where a local generalised method of moments in the spectral domain turns out to be optimal. Asymptotic semiparametric efficiency is established in the Cramer-Rao sense. Main findings are that non-synchronicity of observation times has no impact on the asymptotics and that major efficiency gains are possible under correlation. Simulations illustrate the finite-sample behaviour.

Keywords: adaptive estimation, asymptotic equivalence, asynchronous observations, integrated covolatility matrix, quadratic covariation, semiparametric efficiency, microstructure noise, spectral estimation

JEL Classification: C13, C32, G10

Suggested Citation

Bibinger, Markus and Hautsch, Nikolaus and Malec, Peter and Reiss, Markus, Estimating the Quadratic Covariation Matrix from Noisy Observations: Local Method of Moments and Efficiency (August 25, 2013). Available at SSRN: https://ssrn.com/abstract=2315801 or http://dx.doi.org/10.2139/ssrn.2315801

Markus Bibinger (Contact Author)

University of Mannheim ( email )

Mannheim, 68131
Germany

Nikolaus Hautsch

University of Vienna - Department of Statistics and Operations Research ( email )

Oskar-Morgenstern-Platz 1
Vienna, A-1090
Austria

Center for Financial Studies (CFS) ( email )

Grüneburgplatz 1
Frankfurt am Main, 60323
Germany

Peter Malec

University of Cambridge - Faculty of Economics ( email )

Sidgwick Avenue
Cambridge, CB3 9DD
United Kingdom

Markus Reiss

Humboldt University of Berlin ( email )

Berlin, 10099
Germany

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