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Properties of the nonparametric autoregressive bootstrap

Author

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

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.

Suggested Citation

  • Franke, Jürgen & Kreiss, Jens-Peter & Mammen, Enno & Neumann, Michael H., 1998. "Properties of the nonparametric autoregressive bootstrap," SFB 373 Discussion Papers 1998,54, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:199854
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    File URL: https://www.econstor.eu/bitstream/10419/61278/1/721981283.pdf
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    References listed on IDEAS

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    1. Politis, D. N. & Romano, Joseph P. & Wolf, Michael, 1997. "Subsampling for heteroskedastic time series," Journal of Econometrics, Elsevier, vol. 81(2), pages 281-317, December.
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    Cited by:

    1. Wolfgang Hardle & Torsten Kleinow & Alexander Korostelev & Camille Logeay & Eckhard Platen, 2008. "Semiparametric diffusion estimation and application to a stock market index," Quantitative Finance, Taylor & Francis Journals, vol. 8(1), pages 81-92.

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