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Block Bootstrap and Long Memory

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  • George Kapetanios

    ()
    (Queen Mary, University of London)

  • Fotis Papailias

    (Queen Mary, University of London)

Abstract

We consider the issue of Block Bootstrap methods in processes that exhibit strong dependence. The main difficulty is to transform the series in such way that implementation of these techniques can provide an accurate approximation to the true distribution of the test statistic under consideration. The bootstrap algorithm we suggest consists of the following operations: given x t ~ I(d 0) , 1) estimate the long memory parameter and obtain dˆ , 2) difference the series dˆ times, 3) apply the block bootstrap on the above and finally, 4) cumulate the bootstrap sample dˆ times. Repetition of steps 3 and 4 for a sufficient number of times, results to a successful estimation of the distribution of the test statistic. Furthermore, we establish the asymptotic validity of this method. Its finite-sample properties are investigated via Monte Carlo experiments and the results indicate that it can be used as an alternative, and in most of the cases to be preferred than the Sieve AR bootstrap for fractional processes.

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Bibliographic Info

Paper provided by Queen Mary, University of London, School of Economics and Finance in its series Working Papers with number 679.

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Date of creation: Jun 2011
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Handle: RePEc:qmw:qmwecw:wp679

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Keywords: Block Bootstrap; Long memory; Resampling; Strong dependence;

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References

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  1. D. S. Poskitt, 2008. "Properties of the Sieve Bootstrap for Fractionally Integrated and Non-Invertible Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 224-250, 03.
  2. Violetta Dalla & Liudas Giraitis & Javier Hidalgo, 2006. "Consistent estimation of the memory parameter for nonlinear time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(2), pages 211-251, 03.
  3. Andrew Patton & Dimitris Politis & Halbert White, 2009. "Correction to “Automatic Block-Length Selection for the Dependent Bootstrap” by D. Politis and H. White," Econometric Reviews, Taylor & Francis Journals, vol. 28(4), pages 372-375.
  4. Hidalgo, Javier, 2003. "An alternative bootstrap to moving blocks for time series regression models," Journal of Econometrics, Elsevier, vol. 117(2), pages 369-399, December.
  5. Kapetanios, George, 2009. "Testing for strict stationarity in financial variables," Journal of Banking & Finance, Elsevier, vol. 33(12), pages 2346-2362, December.
  6. Donald W.K. Andrews & Offer Lieberman, 2002. "Higher-order Improvements of the Parametric Bootstrap for Long-memory Gaussian Processes," Cowles Foundation Discussion Papers 1378, Cowles Foundation for Research in Economics, Yale University.
  7. 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.
  8. Javier Hidalgo, 2003. "An Alternative Bootstrap to Moving Blocks for Time Series Regression Models," STICERD - Econometrics Paper Series /2003/452, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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Cited by:
  1. Adam McCloskey, 2013. "Estimation of the long-memory stochastic volatility model parameters that is robust to level shifts and deterministic trends," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 285-301, 05.

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