Estimating the quadratic covariation matrix from noisy observations: Local method of moments and efficiency

Markus Bibinger, Nikolaus Hautsch, Peter Malec and Markus Reiss

No 2013-017, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

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 Cramér-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 (search for similar items in EconPapers)
JEL-codes: C14 C32 C58 G10 (search for similar items in EconPapers)
Date: 2013
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