title: Properties of the Nonparametric Autoregressive Bootstrap
creator: Franke, Jürgen
creator: Kreiss, Jens-Peter
creator: Mammen, Enno
creator: Neumann, Michael H.
subject: ddc-510
subject: 510 Mathematics
description: 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.
date: 1998-10-26
type: Working paper
type: info:eu-repo/semantics/workingPaper
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/20796/1/beitrag.52.pdf
identifier: DOI:10.11588/heidok.00020796
identifier: urn:nbn:de:bsz:16-heidok-207960
identifier:   Franke, Jürgen ; Kreiss, Jens-Peter ; Mammen, Enno ; Neumann, Michael H.  (1998) Properties of the Nonparametric Autoregressive Bootstrap.  [Working paper]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/20796/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng