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Multipower variation from generalized difference for fractional integral processes with jumps

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  • Guangying Liu
  • Lixin Zhang
  • Xinian Fang

Abstract

This article presents limit theorems of the multipower variation based on a generalized difference for the fractional integral process with jumps observed in high frequency. In particular, we obtain the large number laws for threshold multipower variation and multipower variation and the associated central limit theorems. The limit theorems are applied to estimate Hurst parameter, and the consistence and asymptotic distribution of the estimator are established. These results will provide some new statistical tools to analyze long-memory effect in high-frequency situation.

Suggested Citation

  • Guangying Liu & Lixin Zhang & Xinian Fang, 2017. "Multipower variation from generalized difference for fractional integral processes with jumps," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(19), pages 9662-9678, October.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:19:p:9662-9678
    DOI: 10.1080/03610926.2016.1217019
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