Functional stable limit theorems for quasi-efficient spectral covolatility estimators

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

Altmeyer, Randolf¹  Bibinger, Markus¹ 

[1] Humboldt Univ, Inst Math, D-10099 Berlin, Germany

关键词: Adaptive estimation;    Asymptotic efficiency;    Local parametric estimation;    Microstructure noise;    Integrated volatility;    Non-synchronous observations;   

DOI  :  10.1016/j.spa.2015.07.009

来源: Elsevier

【 摘 要 】

We consider noisy non-synchronous discrete observations of a continuous semimartingale with random volatility. Functional stable central limit theorems are established under high-frequency asymptotics in three setups: one-dimensional for the spectral estimator of integrated volatility, from two-dimensional asynchronous observations for a bivariate spectral covolatility estimator and multivariate for a local method of moments. The results demonstrate that local adaptivity and smoothing noise dilution in the Fourier domain facilitate substantial efficiency gains compared to previous approaches. In particular, the derived asymptotic variances coincide with the benchmarks of semiparametric Cramer Rao lower bounds and the considered estimators are thus asymptotically efficient in idealized sub-experiments. Feasible central limit theorems allowing for confidence bounds are provided. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

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