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

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  • Kato, Kengo
  • Kurisu, Daisuke

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.

Suggested Citation

  • Kato, Kengo & Kurisu, Daisuke, 2020. "Bootstrap confidence bands for spectral estimation of Lévy densities under high-frequency observations," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1159-1205.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:3:p:1159-1205
    DOI: 10.1016/j.spa.2019.04.012
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