Multipower variation from generalized difference for fractional integral processes with jumps

Guangying Liu, Lixin Zhang and Xinian Fang

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 19, 9662-9678

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.

Date: 2017
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DOI: 10.1080/03610926.2016.1217019

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