Limit Theorems for Power Variations of Pure-Jump Processes with Application to Activity Estimation
36 Pages Posted: 6 Oct 2010
Date Written: March 18, 2010
This paper derives the asymptotic behavior of realized power variation of pure-jump Ito 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 efficient adaptive estimator for the activity of discretely-sampled Ito semimartingale over a fixed interval.
Keywords: Activity Index, Blumenthal-Getoor Index, Central Limit Theorem, Ito Semimartingale, High-Frequency Data, Jumps, Realized Power Variation
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