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Title: Bootstrap confidence bands for spectral estimation of Levy densities under high-frequency observations Authors:  Daisuke Kurisu - Tokyo Institute of Technology (Japan) [presenting]
Kengo Kato - University of Tokyo (Japan)
Abstract: Bootstrap methods are developed to construct uniform confidence bands for nonparametric spectral estimation of L\'{e}vy densities under high-frequency observations. We are given $n$ discrete observations at frequency $1/\Delta$, and assume that $\Delta = \Delta_{n} \to 0$ and $n\Delta \to \infty$ as $n \to \infty$. We employ a spectral estimator of the L\'{e}vy 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 simulation studies.