Nonparametric estimation of the volatility under microstructure noise: wavelet adaptation
AbstractWe study nonparametric estimation of the volatility function of a diffusion process from discrete data, when the data are blurred by additional noise. This noise can be white or correlated, and serves as a model for microstructure effects in financial modeling, when the data are given on an intra-day scale. By developing pre-averaging techniques combined with wavelet thresholding, we construct adaptive estimators that achieve a nearly optimal rate within a large scale of smoothness constraints of Besov type. Since the underlying signal (the volatility) is genuinely random, we propose a new criterion to assess the quality of estimation; we retrieve the usual minimax theory when this approach is restricted to deterministic volatility.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 24562.
Date of creation: 27 Jul 2010
Date of revision:
Adaptive estimation; diffusion processes; high-frequency data; microstructure noise; minimax estimation; semimartingales; wavelets.;
Find related papers by JEL classification:
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C0 - Mathematical and Quantitative Methods - - General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-08-28 (All new papers)
- NEP-ECM-2010-08-28 (Econometrics)
- NEP-ETS-2010-08-28 (Econometric Time Series)
- NEP-MST-2010-08-28 (Market Microstructure)
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