Bipower-type estimation in a noisy diffusion setting

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Podolskij, Mark²  Vetter, Mathias¹ 

[1] Ruhr Univ Bochum, Fak Math, D-44780 Bochum, Germany

[2] ETH, Dept Math, CH-8092 Zurich, Switzerland

关键词: Bipower variation;    Central limit theorem;    High-frequency data;    Microstructure noise;    Quadratic variation;    Semimartingale theory;    Test for jumps;   

DOI  :  10.1016/j.spa.2009.02.006

来源: Elsevier

【 摘 要 】

We consider a new class of estimators for volatility functionals in the setting of frequently observed Ito diffusions which are disturbed by i.i.d. noise. These statistics extend the approach of pre-averaging as a general method for the estimation of the integrated volatility in the presence of microstructure noise and are closely related to the original concept of bipower variation in the no-noise case. We show that this approach provides efficient estimators for a large class of integrated powers of volatility and prove the associated (stable) central limit theorems. In a more general Ito semimartingale framework this method can be used to define both estimators for the entire quadratic variation of the underlying process and jump-robust estimators which are consistent for various functionals of volatility. As a by-product we obtain a simple test for the presence of jumps in the underlying semimartingale. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free