Abstract
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.
Original language | English (US) |
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Pages (from-to) | 546-588 |
Number of pages | 43 |
Journal | Annals of Applied Probability |
Volume | 21 |
Issue number | 2 |
DOIs | |
State | Published - Apr 1 2011 |
Keywords
- Activity index
- Blumenthal-Getoor index
- Central limit theorem
- High-frequency data
- Itô semimartingale
- Jumps
- Realized power variation
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty