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A0715
Title: Bootstrap confidence bands for Levy densities under high-frequency observations Authors:  Daisuke Kurisu - The University of Tokyo (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 assume that we observe $n$ discrete observations at frequency $1/\Delta$ with $\Delta > 0$, and work with the high-frequency setup where $\Delta = \Delta_{n} \to 0$ 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 Gaussian multiplier (or wild) and empirical (or Efron's) bootstraps to construct confidence bands for the spectral estimator on a compact set that does not intersect the origin. We provide conditions under which the proposed confidence bands are asymptotically valid. Our confidence bands are shown to be asymptotically valid for a wide class of L\'{e}vy processes. We also develop a practical method for bandwidth selection, and conduct simulation studies to investigate the finite sample performance of the proposed confidence bands.