The Annals of Statistics
- Ann. Statist.
- Volume 42, Number 4 (2014), 1312-1346.
Estimating the quadratic covariation matrix from noisy observations: Local method of moments and efficiency
Markus Bibinger, Nikolaus Hautsch, Peter Malec, and Markus Reiß
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 Cramér–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.
Article information
Source
Ann. Statist., Volume 42, Number 4 (2014), 1312-1346.
Dates
First available in Project Euclid: 25 June 2014
Permanent link to this document
https://projecteuclid.org/euclid.aos/1403715202
Digital Object Identifier
doi:10.1214/14-AOS1224
Mathematical Reviews number (MathSciNet)
MR3226158
Zentralblatt MATH identifier
1302.62190
Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62G05: Estimation
Keywords
Asymptotic equivalence asynchronous observations integrated covolatility matrix high-frequency data semi-parametric efficiency microstructure noise
Citation
Bibinger, Markus; Hautsch, Nikolaus; Malec, Peter; Reiß, Markus. Estimating the quadratic covariation matrix from noisy observations: Local method of moments and efficiency. Ann. Statist. 42 (2014), no. 4, 1312--1346. doi:10.1214/14-AOS1224. https://projecteuclid.org/euclid.aos/1403715202
Supplemental materials
- Lower bound proofs for estimating the quadratic covariation matrix from noisy observations. We provide detailed proofs for Section 5.Digital Object Identifier: doi:10.1214/14-AOS1224SUPP