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Bootstrap confidence bands for spectral estimation of Lévy densities under high-frequency observations

Kengo Kato and Daisuke Kurisu

Stochastic Processes and their Applications, 2020, vol. 130, issue 3, 1159-1205

Abstract: This paper develops bootstrap methods to construct uniform confidence bands for nonparametric spectral estimation of Lévy densities under high-frequency observations. We are given n discrete observations at frequency 1∕Δ, and assume that Δ=Δn→0 and nΔ→∞ as n→∞. We employ a spectral estimator of the Lévy density, and develop novel implementations of multiplier and empirical bootstraps to construct confidence bands on a compact set away from the origin. We provide conditions under which the confidence bands are asymptotically valid. We also develop a practical method for bandwidth selection, and conduct numerical studies.

Keywords: Empirical bootstrap; High-frequency data; Lévy process; Multiplier bootstrap; Spectral estimation (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2019.04.012

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