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Bias Reduction of Long Memory Parameter Estimators via the Pre-filtered Sieve Bootstrap

  • D.S. Poskitt

    ()

  • Gael M. Martin

    ()

  • Simone D. Grose

    ()

This paper investigates the use of bootstrap-based bias correction of semi-parametric estimators of the long memory parameter in fractionally integrated processes. The re-sampling method involves the application of the sieve bootstrap to data pre-filtered by a preliminary semi-parametric estimate of the long memory parameter. Theoretical justification for using the bootstrap techniques to bias adjust log periodogram and semi-parametric local Whittle estimators of the memory parameter is provided. Simulation evidence comparing the performance of the bootstrap bias correction with analytical bias correction techniques is also presented. The bootstrap method is shown to produce notable bias reductions, in particular when applied to an estimator for which analytical adjustments have already been used. The empirical coverage of confidence intervals based on the bias-adjusted estimators is very close to the nominal, for a reasonably large sample size, more so than for the comparable analytically adjusted estimators. The precision of inferences (as measured by interval length) is also greater when the bootstrap is used to bias correct rather than analytical adjustments.

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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 8/12.

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Length: 37 pages
Date of creation: Apr 2012
Date of revision:
Handle: RePEc:msh:ebswps:2012-8
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  1. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
  2. Doornik, Jurgen A. & Ooms, Marius, 2003. "Computational aspects of maximum likelihood estimation of autoregressive fractionally integrated moving average models," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 333-348, March.
  3. Faÿ, Gilles & Moulines, Eric & Soulier, Philippe, 2004. "Edgeworth expansions for linear statistics of possibly long-range-dependent linear processes," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 275-288, February.
  4. S. D. Grose & D. S. Poskitt, 2006. "The Finite-Sample Properties of Autoregressive Approximations of Fractionally-Integrated and Non-Invertible Processes," Monash Econometrics and Business Statistics Working Papers 15/06, Monash University, Department of Econometrics and Business Statistics.
  5. Poskitt, D.S., 1994. "A Note on Autoregressive Modeling," Econometric Theory, Cambridge University Press, vol. 10(05), pages 884-899, December.
  6. D.S. Poskitt & Simone D. Grose & Gael M. Martin, 2013. "Higher-Order Improvements of the Sieve Bootstrap for Fractionally Integrated Processes," Monash Econometrics and Business Statistics Working Papers 25/13, Monash University, Department of Econometrics and Business Statistics.
  7. 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.
  8. Donald W.K. Andrews & Patrik Guggenberger, 2000. "A Bias-Reduced Log-Periodogram Regression Estimator for the Long-Memory Parameter," Cowles Foundation Discussion Papers 1263, Cowles Foundation for Research in Economics, Yale University.
  9. 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.
  10. Morten Ørregaard Nielsen & Per Houmann Frederiksen, 2005. "Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 405-443.
  11. Donald W. K. Andrews & Yixiao Sun, 2004. "Adaptive Local Polynomial Whittle Estimation of Long-range Dependence," Econometrica, Econometric Society, vol. 72(2), pages 569-614, 03.
  12. Offer Lieberman, 2001. "The Exact Bias Of The Log-Periodogram Regression Estimator," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 369-383.
  13. Inoue, Akihiko & Kasahara, Yukio, 2004. "Partial autocorrelation functions of the fractional ARIMA processes with negative degree of differencing," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 135-147, April.
  14. 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.
  15. Edwin Choi & Peter Hall, 2000. "Bootstrap confidence regions computed from autoregressions of arbitrary order," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 461-477.
  16. 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.
  17. D. Poskitt, 2007. "Autoregressive approximation in nonstandard situations: the fractionally integrated and non-invertible cases," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(4), pages 697-725, December.
  18. Faÿ, Gilles, 2010. "Moment bounds for non-linear functionals of the periodogram," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 983-1009, June.
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