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August 2011 On the range of validity of the autoregressive sieve bootstrap
Jens-Peter Kreiss, Efstathios Paparoditis, Dimitris N. Politis
Ann. Statist. 39(4): 2103-2130 (August 2011). DOI: 10.1214/11-AOS900


We explore the limits of the autoregressive (AR) sieve bootstrap, and show that its applicability extends well beyond the realm of linear time series as has been previously thought. In particular, for appropriate statistics, the AR-sieve bootstrap is valid for stationary processes possessing a general Wold-type autoregressive representation with respect to a white noise; in essence, this includes all stationary, purely nondeterministic processes, whose spectral density is everywhere positive. Our main theorem provides a simple and effective tool in assessing whether the AR-sieve bootstrap is asymptotically valid in any given situation. In effect, the large-sample distribution of the statistic in question must only depend on the first and second order moments of the process; prominent examples include the sample mean and the spectral density. As a counterexample, we show how the AR-sieve bootstrap is not always valid for the sample autocovariance even when the underlying process is linear.


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Jens-Peter Kreiss. Efstathios Paparoditis. Dimitris N. Politis. "On the range of validity of the autoregressive sieve bootstrap." Ann. Statist. 39 (4) 2103 - 2130, August 2011.


Published: August 2011
First available in Project Euclid: 26 October 2011

zbMATH: 1227.62067
MathSciNet: MR2893863
Digital Object Identifier: 10.1214/11-AOS900

Primary: 62M10 , 62M15
Secondary: 62G09

Keywords: Autoregression , bootstrap , time series

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.39 • No. 4 • August 2011
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