Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/61278
Authors: 
Franke, Jürgen
Kreiss, Jens-Peter
Mammen, Enno
Neumann, Michael H.
Year of Publication: 
1998
Series/Report no.: 
Discussion Papers, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1998,54
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 particular estimators 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.
Subjects: 
Bootstrap
nonparametric autoregression
coupling
geometric ergodicity
consistence
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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