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A Bootstrap Theory for Weakly Integrated Processes

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  • Park, Joon

    (Rice U)

Abstract

This paper develops a bootstrap theory for models including autoregressive time series with roots approaching to unity as the sample size increases. In particular, we consider the processes with roots converging to unity with rates slower than n?1. We call such processes weakly integrated processes. It is established that the bootstrap relying on the estimated autoregressive model is generally consistent for the weakly integrated processes. Both the sample and bootstrap statistics of the weakly integrated processes are shown to yield the same normal asymptotics. Moreover, for the asymptotically pivotal statistics of the weakly integrated processes, the bootstrap is expected to provide an asymptotic refinement and give better approximations for the finite sample distributions than the first order asymptotic theory. For the weakly integrated processes, the magnitudes of potential refinements by the bootstrap are shown to be proportional to the rate at which the root of the underlying process converges to unity. The order of boostrap refinement can be as large as o(n-1/2+_) for any espial > 0. Our theory helps to explain the actual improvements observed by many practitioners, which are made by the use of the bootstrap in analyzing the models with roots close to unity.

Suggested Citation

  • Park, Joon, 2003. "A Bootstrap Theory for Weakly Integrated Processes," Working Papers 2003-16, Rice University, Department of Economics.
  • Handle: RePEc:ecl:riceco:2003-16
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    File URL: http://www.ruf.rice.edu/~econ/papers/2003papers/16park.pdf
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    References listed on IDEAS

    as
    1. Park, Joon, 2003. "Weak Unit Roots," Working Papers 2003-17, Rice University, Department of Economics.
    2. Atsushi Inoue & Lutz Kilian, 2002. "Bootstrapping Autoregressive Processes with Possible Unit Roots," Econometrica, Econometric Society, vol. 70(1), pages 377-391, January.
    3. Joon Y. Park, 2003. "Bootstrap Unit Root Tests," Econometrica, Econometric Society, vol. 71(6), pages 1845-1895, November.
    4. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, July.
    5. Chang, Yoosoon & Park, Joon Y. & Song, Kevin, 2006. "Bootstrapping cointegrating regressions," Journal of Econometrics, Elsevier, vol. 133(2), pages 703-739, August.
    6. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    7. Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
    8. Nankervis, John C & Savin, N E, 1996. "The Level and Power of the Bootstrap t Test in the AR(1) Model with Trend," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 161-168, April.
    9. Park, Joon Y., 2002. "An Invariance Principle For Sieve Bootstrap In Time Series," Econometric Theory, Cambridge University Press, vol. 18(02), pages 469-490, April.
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    Cited by:

    1. Skrobotov Anton, 2018. "On Bootstrap Implementation of Likelihood Ratio Test for a Unit Root," Working Papers wpaper-2018-302, Gaidar Institute for Economic Policy, revised 2018.
    2. Westerlund J. & Smeekes S., 2013. "Robust block bootstrap panel predictability tests," Research Memorandum 060, Maastricht University, Graduate School of Business and Economics (GSBE).
    3. Marcus J. Chambers & Maria Kyriacou, 2018. "Jackknife Bias Reduction in the Presence of a Near-Unit Root," Econometrics, MDPI, Open Access Journal, vol. 6(1), pages 1-28, March.
    4. Westerlund, Joakim & Thuraisamy, Kannan, 2016. "Panel multi-predictor test procedures with an application to emerging market sovereign risk," Emerging Markets Review, Elsevier, vol. 28(C), pages 44-60.
    5. Sizova, Natalia, 2014. "A frequency-domain alternative to long-horizon regressions with application to return predictability," Journal of Empirical Finance, Elsevier, vol. 28(C), pages 261-272.
    6. Shibamoto, Masahiko, 2008. "The estimation of monetary policy reaction function in a data-rich environment: The case of Japan," Japan and the World Economy, Elsevier, vol. 20(4), pages 497-520, December.
    7. Khalaf, Lynda & Urga, Giovanni, 2014. "Identification robust inference in cointegrating regressions," Journal of Econometrics, Elsevier, vol. 182(2), pages 385-396.

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