Limit Theorems for Power Variations of Pure-jump Processes with Application to Activity Estimation

@inproceedings{Todorov2010LimitTF,
  title={Limit Theorems for Power Variations of Pure-jump Processes with Application to Activity Estimation},
  author={Viktor Todorov and George Tauchen},
  year={2010}
}
This paper derives the asymptotic behavior of realized power variation of pure-jump Itô 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 Itô semimartingale over a fixed interval. 
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