Open Access
August 2020 Extending the validity of frequency domain bootstrap methods to general stationary processes
Marco Meyer, Efstathios Paparoditis, Jens-Peter Kreiss
Ann. Statist. 48(4): 2404-2427 (August 2020). DOI: 10.1214/19-AOS1892


Existing frequency domain methods for bootstrapping time series have a limited range. Essentially, these procedures cover the case of linear time series with independent innovations, and some even require the time series to be Gaussian. In this paper we propose a new frequency domain bootstrap method—the hybrid periodogram bootstrap (HPB)—which is consistent for a much wider range of stationary, even nonlinear, processes and which can be applied to a large class of periodogram-based statistics. The HPB is designed to combine desirable features of different frequency domain techniques while overcoming their respective limitations. It is capable to imitate the weak dependence structure of the periodogram by invoking the concept of convolved subsampling in a novel way that is tailor-made for periodograms. We show consistency for the HPB procedure for a general class of stationary time series, ranging clearly beyond linear processes, and for spectral means and ratio statistics on which we mainly focus. The finite sample performance of the new bootstrap procedure is illustrated via simulations.


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Marco Meyer. Efstathios Paparoditis. Jens-Peter Kreiss. "Extending the validity of frequency domain bootstrap methods to general stationary processes." Ann. Statist. 48 (4) 2404 - 2427, August 2020.


Received: 1 December 2018; Revised: 1 May 2019; Published: August 2020
First available in Project Euclid: 14 August 2020

MathSciNet: MR4134800
Digital Object Identifier: 10.1214/19-AOS1892

Primary: 62M10 , 62M15
Secondary: 62G09

Keywords: bootstrap , periodogram , spectral means , Stationary processes

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 4 • August 2020
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