Limit Theorems for Power Variations of Pure-Jump Processes with Application to Activity Estimation
AbstractThis paper derives the asymptotic behavior of realized power variation of pure-jump It^o semimartingales as the sampling frequency within a fixed interval increases to infinity. We prove convergence in probability and an associated central limit theorem for the realized power variation as a function of its power. We apply the limit theorems to propose an e±cient adaptive estimator for the activity of discretely-sampled It^o semimartingale over a fixed interval.
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Bibliographic InfoPaper provided by Duke University, Department of Economics in its series Working Papers with number 10-74.
Date of creation: 2010
Date of revision:
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Postal: Department of Economics Duke University 213 Social Sciences Building Box 90097 Durham, NC 27708-0097
Phone: (919) 660-1800
Fax: (919) 684-8974
Web page: http://econ.duke.edu/
Activity index; Blumenthal-Getoor index; Central Limit Theorem; It^o semimartingale; high-frequency data; jumps; realized power variation;
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- Jing, Bing-Yi & Kong, Xin-Bing & Liu, Zhi & Mykland, Per, 2012. "On the jump activity index for semimartingales," Journal of Econometrics, Elsevier, vol. 166(2), pages 213-223.
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