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Properties of the Nonparametric Autoregressive Bootstrap

Franke, Jürgen ; Kreiss, Jens-Peter ; Mammen, Enno ; Neumann, Michael H.

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Abstract

We prove geometric ergodicity and absolute regularity of the nonparametric autoregressive bootstrap process. To this end, we revisit this problem for nonparametric autoregressive processes and give some quantitative conditions (i.e., with explicit constants) under which the mixing coefficients of such processes can be bounded by some exponentially decaying sequence. This is achieved by using well-established coupling techniques.Then we apply the result to the bootstrap process and propose some particularestimators of the autoregression function and of the density of the innovations for which the bootstrap process has the desired properties.Moreover, by using some "decoupling" argument, we show that the stationary density of the bootstrap process converges to that of the original process. As an illustration, we use the proposed bootstrap method to construct simultaneous confidence bands and supremum-type tests for the autoregression function as well as to approximate the distribution of the least squares estimator in a certain parametric model.

Item Type: Working paper
Place of Publication: Heidelberg
Date Deposited: 30 May 2016 08:47
Date: 26 October 1998
Number of Pages: 26
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 510 Mathematics
Uncontrolled Keywords: Bootstrap, nonparametric autoregression, coupling, geometric ergodicity, consistence
Schriftenreihe ID: Beiträge zur Statistik > Beiträge
Additional Information: auch veröffentlicht in: Journal of Time Series Analysis Volume 23, Issue 5, pages 555–585, September 2002
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