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A note on the central limit theorem for bipower variation of general functions

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  • Kinnebrock, Silja
  • Podolskij, Mark

Abstract

In 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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Article provided by Elsevier in its journal Stochastic Processes and their Applications.

Volume (Year): 118 (2008)
Issue (Month): 6 (June)
Pages: 1056-1070

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Handle: RePEc:eee:spapps:v:118:y:2008:i:6:p:1056-1070

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Keywords: Bipower variation Central limit theorem Diffusion models High-frequency data Semimartingale theory;

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