Empirical likelihood for high frequency data

Lorenzo Camponovo, Yukitoshi Matsushita and Taisuke Otsu

Journal of Business & Economic Statistics, 2020, vol. 38, issue 3, 621-632

Abstract: 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.

Date: 2020
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DOI: 10.1080/07350015.2018.1549051

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