A note on the central limit theorem for bipower variation of general functions
AbstractIn this paper we present a central limit theorem for general functions of the increments of Brownian semimartingales. This provides a natural extension of the results derived in [O.E. Barndorff-Nielsen, S.E. Graversen, J. Jacod, M. Podolskij, N. Shephard, A central limit theorem for realised power and bipower variations of continuous semimartingales, in: From Stochastic Analysis to Mathematical Finance, Festschrift for Albert Shiryaev, Springer, 2006], where the central limit theorem was shown for even functions. We prove an infeasible central limit theorem for general functions and state some assumptions under which a feasible version of our results can be obtained. Finally, we present some examples from the literature to which our theory can be applied.
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Bibliographic InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 118 (2008)
Issue (Month): 6 (June)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
Other versions of this item:
- Silja Kinnebrock & Mark Podolskij, 2007. "A Note on the Central Limit Theorem for Bipower Variation of General Functions," OFRC Working Papers Series 2007fe03, Oxford Financial Research Centre.
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