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Properties of the Sieve Bootstrap for Fractionally Integrated and Non-Invertible Processes

  • D. S. Poskitt

    ()

In this paper we will investigate the consequences of applying the sieve bootstrap under regularity conditions that are sufficiently general to encompass both fractionally integrated and non-invertible processes. The sieve bootstrap is obtained by approximating the data generating process by an autoregression whose order h increases with the sample size T. The sieve bootstrap may be particularly useful in the analysis of fractionally integrated processes since the statistics of interest can often be non-pivotal with distributions that depend on the fractional index d. The validity of the sieve bootstrap is established and it is shown that when the sieve bootstrap is used to approximate the distribution of a general class of statistics admitting an Edgeworth expansion then the error rate achieved is of order O (T  β+d-1 ), for any β > 0. Practical implementation of the sieve bootstrap is considered and the results are illustrated using a canonical example.

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2006/wp12-06.pdf
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Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 12/06.

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Length: 27 pages
Date of creation: Jul 2006
Date of revision:
Handle: RePEc:msh:ebswps:2006-12
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  1. L. Giraitis & P.M. Robinson, 2003. "Edgeworth expansions for semiparametric Whittle estimation of long memory," LSE Research Online Documents on Economics 291, London School of Economics and Political Science, LSE Library.
  2. Liudas Giraitis & Peter M Robinson, 2002. "Edgeworth Expansions for Semiparametric Whittle Estimation of Long Memory," STICERD - Econometrics Paper Series /2002/438, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  3. Donald W.K. Andrews, 2002. "The Block-block Bootstrap: Improved Asymptotic Refinements," Cowles Foundation Discussion Papers 1370, Cowles Foundation for Research in Economics, Yale University.
  4. Hosking, Jonathan R. M., 1996. "Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series," Journal of Econometrics, Elsevier, vol. 73(1), pages 261-284, July.
  5. Lieberman, Offer & Phillips, Peter C.B., 2004. "Expansions For The Distribution Of The Maximum Likelihood Estimator Of The Fractional Difference Parameter," Econometric Theory, Cambridge University Press, vol. 20(03), pages 464-484, June.
  6. Joel L. Horowitz, 2003. "Bootstrap Methods for Markov Processes," Econometrica, Econometric Society, vol. 71(4), pages 1049-1082, 07.
  7. Lieberman, Offer & Rousseau, Judith & Zucker, David M., 2001. "Valid Edgeworth Expansion For The Sample Autocorrelation Function Under Long Range Dependence," Econometric Theory, Cambridge University Press, vol. 17(01), pages 257-275, February.
  8. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
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