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Abstract
In this paper we introduce a class of statistics for the functional estimation of the spot volatility in the setting of frequency observed diffusion processes which may be disturbed by microstructure noise. We show that the limit theorems for the estimation of the spot volatility and the cross spot volatility of the statistics are still valid even if we add jump processes of finite or infinite activity to the underlying diffusion process. These statistics extend the quadratic variational approach and are related to the concept of multipower variation, which is used in the problem of estimating the integrated volatility.
Received: 2009-06-10
Revised: 2009-10-06
Published Online: 2010-01-25
Published in Print: 2009-December
© de Gruyter 2009
