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Spectral bootstrap confidence bands for Lévy-driven moving average processes (2211.06592v1)
Published 12 Nov 2022 in math.ST, stat.ME, and stat.TH
Abstract: In this paper we study the problem of constructing bootstrap confidence intervals for the L\'evy density of the driving L\'evy process based on high-frequency observations of a L\'evy-driven moving average processes. Using a spectral estimator of the L\'evy density, we propose a novel implementations of multiplier and empirical bootstraps to construct confidence bands on a compact set away from the origin. We also provide conditions under which the confidence bands are asymptotically valid.