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.