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Functional stable limit theorems for quasi-efficient spectral covolatility estimators

Randolf Altmeyer and Markus Bibinger

Stochastic Processes and their Applications, 2015, vol. 125, issue 12, 4556-4600

Abstract: 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 Cramér–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.

Keywords: Adaptive estimation; Asymptotic efficiency; Local parametric estimation; Microstructure noise; Integrated volatility; Non-synchronous observations (search for similar items in EconPapers)
Date: 2015
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