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

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  • D. S. Poskitt

Abstract

In this article, we 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 for |d| 0. Practical implementation of the sieve bootstrap is considered and the results are illustrated using a canonical example. Copyright 2007 The Author

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File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9892.2007.00554.x
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Bibliographic Info

Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

Volume (Year): 29 (2008)
Issue (Month): 2 (03)
Pages: 224-250

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Handle: RePEc:bla:jtsera:v:29:y:2008:i:2:p:224-250

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References

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  1. 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.
  2. 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.
  3. 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.
  4. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
  5. 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.
  6. 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.
  7. Joel L. Horowitz, 2003. "Bootstrap Methods for Markov Processes," Econometrica, Econometric Society, vol. 71(4), pages 1049-1082, 07.
  8. 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.
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Citations

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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.
  2. Nuno Cassola & Claudio Morana, 2007. "Comovements in Volatility in the Euro Money Market," ICER Working Papers 7-2007, ICER - International Centre for Economic Research.
  3. Beran, Jan & Shumeyko, Yevgen, 2012. "Bootstrap testing for discontinuities under long-range dependence," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 322-347.
  4. Simone D. Grose & Gael M. Martin & Donald S. Poskitt, 2013. "Bias Correction of Persistence Measures in Fractionally Integrated Models," Monash Econometrics and Business Statistics Working Papers 29/13, Monash University, Department of Econometrics and Business Statistics.
  5. Rupasinghe, Maduka & Samaranayake, V.A., 2012. "Asymptotic properties of sieve bootstrap prediction intervals for FARIMA processes," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2108-2114.
  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. Morana, Claudio, 2009. "On the macroeconomic causes of exchange rate volatility," International Journal of Forecasting, Elsevier, vol. 25(2), pages 328-350.
  8. D.S. Poskitt & Gael M. Martin & Simone D. Grose, 2014. "Bias Reduction of Long Memory Parameter Estimators via the Pre-filtered Sieve Bootstrap," Monash Econometrics and Business Statistics Working Papers 10/14, Monash University, Department of Econometrics and Business Statistics.
  9. George Kapetanios & Fotis Papailias, 2011. "Block Bootstrap and Long Memory," Working Papers 679, Queen Mary, University of London, School of Economics and Finance.
  10. Md Atikur Rahman Khan & D. S. Poskitt, 2013. "Moment tests for window length selection in singular spectrum analysis of short– and long–memory processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(2), pages 141-155, 03.

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