Limit theorems for power variations of pure-jump processes with application to activity estimation

Viktor Todorov; George Tauchen

doi:10.1214/10-aap700

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arXiv · 1104.1064

Limit theorems for power variations of pure-jump processes with application to activity estimation

Viktor Todorov·George Tauchen

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Abstract

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 efficient adaptive estimator for the activity of discretely-sampled It\^{o} semimartingale over a fixed interval.

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BibTeX RIS

Viktor Todorov, George Tauchen. 2011-04-06. Limit theorems for power variations of pure-jump processes with application to activity estimation. https://doi.org/10.1214/10-aap700

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