Functional stable limit theorems for efficient spectral covolatility estimators

Randolf Altmeyer and Markus Bibinger

No 2014-005, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

Abstract: We consider noisy non-synchronous discrete observations of a continuous semimartingale. Functional stable central limit theorems are established under high-frequency asymptotics in three setups: onedimensional 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 Cram'er-Rao lower bounds and the considered estimators are thus asymptotically efficient in idealized sub-experiments. Feasible central limit theorems allowing for confidence are provided.

Keywords: adaptive estimation; asymptotic efficiency; local parametric estimation; microstructure noise; integrated volatility; non-synchronous observations; spectral estimation; stable limit theorem (search for similar items in EconPapers)
JEL-codes: C14 C32 (search for similar items in EconPapers)
Date: 2014
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