Details

Autor(en) / Beteiligte

• Podolskij, Mark
• Vetter, Mathias

Titel

Bipower-type estimation in a noisy diffusion setting

Ist Teil von

• Stochastic processes and their applications, 2009-09, Vol.119 (9), p.2803-2831

Ort / Verlag

Amsterdam: Elsevier B.V

Erscheinungsjahr

2009

Quelle

Access via ScienceDirect (Elsevier)

Beschreibungen/Notizen

• We consider a new class of estimators for volatility functionals in the setting of frequently observed Itō 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 Itō 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.