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Todorov, Viktor; Tauchen, George

Limit theorems for power variations of pure-jump processes with application to activity estimation. (English) Zbl 1215.62088

Ann. Appl. Probab. 21, No. 2, 546-588 (2011).
Summary: 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.

Cited in 22 Documents

MSC:

62M05 Markov processes: estimation; hidden Markov models
62F12 Asymptotic properties of parametric estimators
60G48 Generalizations of martingales
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J60 Diffusion processes

Keywords:

activity index; Blumenthal-Getoor index; central limit theorem; Itô semimartingale; high-frequency data; jumps; realized power variation
PDFBibTeX XMLCite
\textit{V. Todorov} and \textit{G. Tauchen}, Ann. Appl. Probab. 21, No. 2, 546--588 (2011; Zbl 1215.62088)
Full Text: DOI arXiv

References:

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