Limit Theorems for Power Variations of Pure-Jump Processes with Application to Activity Estimation
This 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.
|Date of creation:||2010|
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