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Bootstrapping general first order autoregression

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  • Heimann, Günter
  • Kreiss, Jens-Peter

Abstract

In this paper we consider general first order autoregression, including the stationary, the explosive and the unstable cases. It is well-known in the literature that the usual bootstrap method for the least squares parameter estimator is asymptotically consistent for the stationary and the explosive cases, but does not work in the unstable case, where the parameter value is equal to +1 and or -1. We propose a modified bootstrap method, which turns out to be asymptotically consistent in all possible situations. Furthermore, we derive tests for stationarity and nonstationarity for first order autoregressions. The bootstrap method is used to obtain critical values. Some simulation results are also enclosed.

Suggested Citation

  • Heimann, Günter & Kreiss, Jens-Peter, 1996. "Bootstrapping general first order autoregression," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 87-98, September.
    • Handle: RePEc:eee:stapro:v:30:y:1996:i:1:p:87-98
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    Citations

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    Cited by:

    1. Jeremy Berkowitz & Lutz Kilian, 2000. "Recent developments in bootstrapping time series," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 1-48.
    2. Atsushi Inoue & Lutz Kilian, 2002. "Bootstrapping Autoregressive Processes with Possible Unit Roots," Econometrica, Econometric Society, vol. 70(1), pages 377-391, January.
    3. Agnieszka Jach & Piotr Kokoszka, 2004. "Subsampling Unit Root Tests for Heavy-Tailed Observations," Methodology and Computing in Applied Probability, Springer, vol. 6(1), pages 73-97, March.
    4. Nikolay Gospodinov & Ye Tao, 2011. "Bootstrap Unit Root Tests in Models with GARCH(1,1) Errors," Econometric Reviews, Taylor & Francis Journals, vol. 30(4), pages 379-405, August.
    5. Gospodinov, Nikolay, 2002. "Median unbiased forecasts for highly persistent autoregressive processes," Journal of Econometrics, Elsevier, vol. 111(1), pages 85-101, November.
    6. Ricardo Cao, 1999. "An overview of bootstrap methods for estimating and predicting in time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 95-116, June.
    7. Fu, Ke-Ang & Li, Yuechao & Ng, Andrew Cheuk-Yin, 2013. "Asymptotics for the residual-based bootstrap approximation in nearly nonstationary AR(1) models with possibly heavy-tailed innovations," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2553-2562.
    8. Benkwitz, Alexander & Lütkepohl, Helmut & Neumann, Michael H., 1997. "Problems related to bootstrapping impulse responses of autoregressive processes," SFB 373 Discussion Papers 1997,85, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    9. van Giersbergen, Noud P. A., 2003. "A note on bootstrapping unit root tests in the presence of a non-zero drift," Economics Letters, Elsevier, vol. 78(2), pages 259-265, February.
    10. Horváth, Lajos & Kokoszka, Piotr, 2003. "A bootstrap approximation to a unit root test statistic for heavy-tailed observations," Statistics & Probability Letters, Elsevier, vol. 62(2), pages 163-173, April.

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