Empirical likelihood for high frequency data

This paper introduces empirical likelihood methods for interval estimation and hypothesis testing on volatility measures in some high frequency data environments. We propose a modified empirical likelihood statistic that is asymptotically pivotal under infill asymptotics, where the number of high fr...

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Bibliographic Details
Published in:Journal of business & economic statistics 2020-07, Vol.38 (3), p.621-632
Main Authors: Camponovo, Lorenzo, Matsushita, Yukitoshi, Otsu, Taisuke
Format: Article
Language:English
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Summary:This paper introduces empirical likelihood methods for interval estimation and hypothesis testing on volatility measures in some high frequency data environments. We propose a modified empirical likelihood statistic that is asymptotically pivotal under infill asymptotics, where the number of high frequency observations in a fixed time interval increases to infinity. The proposed statistic is extended to be robust to the presence of jumps and microstructure noise. We also provide an empirical likelihood-based test to detect the presence of jumps. Furthermore, we study higher-order properties of a general family of nonparametric likelihood statistics and show that a particular statistic admits a Bartlett correction: a higher-order refinement to achieve better coverage or size properties. Simulation and a real data example illustrate the usefulness of our approach.
ISSN:0735-0015
1537-2707
DOI:10.1080/07350015.2018.1549051