Spectral estimation of covolatility from noisy observations using local weights

Markus Bibinger and Markus Reiss

No 2011-086, SFB 649 Discussion Papers from Humboldt University Berlin, Collaborative Research Center 649: Economic Risk

Abstract: We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes which are observed discretely with additive observation noise. The eligibility of this approach to lead to an appropriate estimation for time-varying volatilities stems from an asymptotic equivalence of the underlying statistical model to a white noise model with correlation and volatility processes being constant over small intervals. The asymptotic equivalence of the continuous-time and the discrete-time experiments are proved by a construction with linear interpolation in one direction and local means for the other. The new estimator outperforms earlier nonparametric approaches in the considered model. We investigate its finite sample size characteristics in simulations and draw a comparison between the various proposed methods.

Keywords: asymptotic equivalence; covariation; integrated covolatility; microstructure noise; spectral adaptive estimation (search for similar items in EconPapers)
JEL-codes: C14 C32 C58 G10 (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:sfb649:sfb649dp2011-086

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