The Annals of Statistics

Autoregressive-aided periodogram bootstrap for timeseries

Jens-Peter Kreiss and Efstathios Paparoditis

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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.

Article information

Ann. Statist., Volume 31, Number 6 (2003), 1923-1955.

First available in Project Euclid: 16 January 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G09: Resampling methods
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Bootstrap periodogram nonparametric estimators ratio statistics spectral means


Kreiss, Jens-Peter; Paparoditis, Efstathios. Autoregressive-aided periodogram bootstrap for timeseries. Ann. Statist. 31 (2003), no. 6, 1923--1955. doi:10.1214/aos/1074290332.

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