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December 2003 Autoregressive-aided periodogram bootstrap for timeseries
Jens-Peter Kreiss, Efstathios Paparoditis
Ann. Statist. 31(6): 1923-1955 (December 2003). DOI: 10.1214/aos/1074290332


A bootstrap methodology for the periodogram of a stationary process is proposed which is based on a combination of a time domain parametric and a frequency domain nonparametric bootstrap. The parametric fit is used to generate periodogram ordinates that imitate the essential features of the data and the weak dependence structure of the periodogram while a nonparametric (kernel-based) correction is applied in order to catch features not represented by the parametric fit. The asymptotic theory developed shows validity of the proposed bootstrap procedure for a large class of periodogram statistics. For important classes of stochastic processes, validity of the new procedure is also established for periodogram statistics not captured by existing frequency domain bootstrap methods based on independent periodogram replicates.


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Jens-Peter Kreiss. Efstathios Paparoditis. "Autoregressive-aided periodogram bootstrap for timeseries." Ann. Statist. 31 (6) 1923 - 1955, December 2003.


Published: December 2003
First available in Project Euclid: 16 January 2004

zbMATH: 1042.62081
MathSciNet: MR2036395
Digital Object Identifier: 10.1214/aos/1074290332

Primary: 62G09
Secondary: 62M10

Keywords: bootstrap , nonparametric estimators , periodogram , ratio statistics , spectral means

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.31 • No. 6 • December 2003
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