IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb373/199854.html
   My bibliography  Save this paper

Properties of the nonparametric autoregressive bootstrap

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/61278/1/721981283.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    2. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
    3. Franke, Jürgen & Kreiss, Jens-Peter & Mammen, Enno, 1997. "Bootstrap of kernel smoothing in nonlinear time series," SFB 373 Discussion Papers 1997,20, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Neumann, Michael H., 1997. "On robustness of model-based bootstrap schemes in nonparametric time series analysis," SFB 373 Discussion Papers 1997,88, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Neumann, Michael H. & Paparoditis, Efstathios, 1998. "A nonparametric test for the stationary density," SFB 373 Discussion Papers 1998,58, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Neumann, Michael H. & Paparoditis, Efstathios, 2000. "On bootstrapping L2-type statistics in density testing," Statistics & Probability Letters, Elsevier, vol. 50(2), pages 137-147, November.
    3. Geert Bekaert & Robert J. Hodrick, 2001. "Expectations Hypotheses Tests," Journal of Finance, American Finance Association, vol. 56(4), pages 1357-1394, August.
    4. Paulo M. D. C. Parente & Richard J. Smith, 2021. "Quasi‐maximum likelihood and the kernel block bootstrap for nonlinear dynamic models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 377-405, July.
    5. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    6. Battisti, Michele & Gatto, Massimo Del & Parmeter, Christopher F., 2022. "Skill-biased technical change and labor market inefficiency," Journal of Economic Dynamics and Control, Elsevier, vol. 139(C).
    7. Richard H. Clarida & Mark P. Taylor, 2003. "Nonlinear Permanent - Temporary Decompositions in Macroeconomics and Finance," Economic Journal, Royal Economic Society, vol. 113(486), pages 125-139, March.
    8. Bonsoo Koo & Oliver Linton, 2010. "Semiparametric Estimation of Locally Stationary Diffusion Models," STICERD - Econometrics Paper Series 551, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    9. Zhijie Xiao & Oliver Linton & Raymond J. Carroll & E. Mammen, 2002. "More Efficient Kernel Estimation in Nonparametric Regression with Autocorrelated Errors," Cowles Foundation Discussion Papers 1375, Cowles Foundation for Research in Economics, Yale University.
    10. Dabo-Niang, Sophie & Francq, Christian & Zakoïan, Jean-Michel, 2010. "Combining Nonparametric and Optimal Linear Time Series Predictions," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1554-1565.
    11. Karlsen, Hans Arnfinn & Tjostheim, Dag, 1998. "Nonparametric estimation in null recurrent times series," SFB 373 Discussion Papers 1998,50, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    12. Whang, Yoon-Jae & Linton, Oliver, 1999. "The asymptotic distribution of nonparametric estimates of the Lyapunov exponent for stochastic time series," Journal of Econometrics, Elsevier, vol. 91(1), pages 1-42, July.
    13. Park, Byeong U. & Simar, Léopold & Zelenyuk, Valentin, 2017. "Nonparametric estimation of dynamic discrete choice models for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 97-120.
    14. Chen, Xiaohong & Liao, Zhipeng & Sun, Yixiao, 2014. "Sieve inference on possibly misspecified semi-nonparametric time series models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 639-658.
    15. Dichtl, Hubert & Drobetz, Wolfgang, 2011. "Portfolio insurance and prospect theory investors: Popularity and optimal design of capital protected financial products," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1683-1697, July.
    16. Martin Evans and Richard K. Lyons, 2002. "Are Different-Currency Assets Imperfect Substitutes?," Working Papers gueconwpa~02-02-12, Georgetown University, Department of Economics.
    17. Cai, Zongwu, 2003. "Nonparametric estimation equations for time series data," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 379-390, May.
    18. Michel Carbon, 2005. "Frequency Polygons for Random Fields," Working Papers 2005-04, Center for Research in Economics and Statistics.
    19. Chen, Jia & Li, Degui & Linton, Oliver & Lu, Zudi, 2016. "Semiparametric dynamic portfolio choice with multiple conditioning variables," Journal of Econometrics, Elsevier, vol. 194(2), pages 309-318.
    20. Aït-Sahalia, Yacine & Park, Joon Y., 2016. "Bandwidth selection and asymptotic properties of local nonparametric estimators in possibly nonstationary continuous-time models," Journal of Econometrics, Elsevier, vol. 192(1), pages 119-138.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:sfb373:199854. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/sfhubde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.