LIMIT THEOREMS FOR BIPOWER VARIATION IN FINANCIAL ECONOMETRICS

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Abstract
In this paper we provide an asymptotic analysis of generalized bipower measures of the variation of price processes in financial economics. These measures encompass the usual quadratic variation, power variation, and bipower variations that have been highlighted in recent years in financial econometrics. The analysis is carried out under some rather general Brownian semimartingale assumptions, which allow for standard leverage effects.Ole E. Barndorff-Nielsen's work is supported by the Centre for Analytical Finance (CAF), which is funded by the Danish Social Science Research Council. Neil Shephard's research is supported by the UK's ESRC through the grant “High frequency financial econometrics based upon power variation.” We thank the editor, Peter Phillips, and the referees for their stimulating comments on an earlier version.