Bibinger, M., Hautsch, N., Malec, P. and Reiss, M.

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

The Annals of Statistics

Vol. 42 no. 4 pp. 1312-1346 (2014)

Abstract: An efficient estimator is constructed for the quadratic covariation or integrated co-volatility matrix of a multivariate continuous martingale based on noisy and nonsynchronous 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 semi-parametric efficiency is established in the CramÃ©râ€“Rao sense. Main findings are that nonsynchronicity 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: Asympototic equivalence, Asynchronous observations, Integrated covolatility matrix, High frequency data, Semi-parametric efficiency, Microstructure noise

JEL Codes: C13, C32, G10

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Publisher's Link: http://projecteuclid.org/euclid.aos/1403715202