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

By Markus Bibinger, Nikolaus Hautsch, Peter Malec, Markus Reiß. 2013

104 citations recorded by the source corpus.

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 CramA©r-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.

Subfields: Aerospace Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b85277cf25f2cd79c7d2960b8ba695da3e489709

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In Aerospace Engineering

In Statistics and Probability

Citations in the corpus

Estimating the Spot Covariation of Asset Prices—Statistical Theory and Empirical Evidence (2014, methodology): “4) in Bibinger et al. (2014) plus a negligible remainder in the more general model and suggests estimating Σkhn based on the empirical covariance SjkS jk, which is bias-corrected by the noise-induced term π 2j2h−2 n H n k .”
Adaptive estimation of continuous-time regression models using high-frequency data (2017, background): “In the continuous-time limit, it is wellknown that the spot covariance matrix process ct ≡ σtσ t of X can be identified, which we further (1)We leave for future work the analysis of the problem of efficient continuous-time regression estimation in the case when the data is contaminated by noise and ”
Econometrics of co-jumps in high-frequency data with noise (2015, background): “For a continuous martingale observed in noise this fundamental result has been established in Bibinger et al. (2013) by virtue of an asymptotic equivalence in Le Cam’s sense of the experiment with discrete non-synchronous observations and a continuous-time white noise experiment.”
Econometric Analysis of Vast Covariance Matrices Using Composite Realized Kernels and Their Application to Portfolio Choice (2016, background): “…for noise as well as nonsynchronous trading is the focus of Zhang (2011a), Christensen, Kinnebrock, and Podolskij (2010), Aı̈tSahalia, Fan, and Xiu (2010), Park and Linton (2012), Bibinger (2011), Bibinger (2012), Bibinger et al. (2014), Shephard and Xiu (2014), and Barndorff-Nielsen et al. (2011).”
Incorporating Global Industrial Classification Standard Into Portfolio Allocation: A Simple Factor-Based Large Covariance Matrix Estimator With High-Frequency Data (2016, unknown): “Alternatively, the thresholding approach is also very popular, including Bickel and Levina (2008a), Bickel and Levina (2008b), Cai and Liu (2011), etc. Fan and Liu (2013) and Zhou, Cai, and Ren (2014) have a very comprehensive review of this literature.”