Bootstrap confidence bands for spectral estimation of Lévy densities under high-frequency observations
Kengo Kato and
Stochastic Processes and their Applications, 2020, vol. 130, issue 3, 1159-1205
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)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:3:p:1159-1205
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