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Altmeyer, Randolf
Bibinger, Markus
Year of Publication: 
Series/Report no.: 
SFB 649 Discussion Paper 2014-005
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.
adaptive estimation
asymptotic efficiency
local parametric estimation
microstructure noise
integrated volatility
non-synchronous observations
spectral estimation
stable limit theorem
Document Type: 
Working Paper

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