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A Bootstrap Invariance Principle for Highly Nonstationary Long Memory Processes

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  • George Kapetanios

    (Queen Mary, University of London)

Abstract

This paper presents an invariance principle for highly nonstationary long memory processes, defined as processes with long memory parameter lying in (1, 1.5). This principle provides the tools for showing asymptotic validity of the bootstrap in the context of such processes.

Suggested Citation

  • George Kapetanios, 2004. "A Bootstrap Invariance Principle for Highly Nonstationary Long Memory Processes," Working Papers 507, Queen Mary University of London, School of Economics and Finance.
    • Handle: RePEc:qmw:qmwecw:507
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    File URL: https://www.qmul.ac.uk/sef/media/econ/research/workingpapers/2004/items/wp507.pdf
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    References listed on IDEAS

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    1. Inoue, Atsushi & Kilian, Lutz, 2003. "The Continuity Of The Limit Distribution In The Parameter Of Interest Is Not Essential For The Validity Of The Bootstrap," Econometric Theory, Cambridge University Press, vol. 19(6), pages 944-961, December.
    2. Andrews, Donald W.K. & Lieberman, Offer & Marmer, Vadim, 2006. "Higher-order improvements of the parametric bootstrap for long-memory Gaussian processes," Journal of Econometrics, Elsevier, vol. 133(2), pages 673-702, August.
    3. 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.
    4. Hidalgo, Javier, 2003. "An alternative bootstrap to moving blocks for time series regression models," LSE Research Online Documents on Economics 6850, London School of Economics and Political Science, LSE Library.
    5. Javier Hidalgo, 2003. "An Alternative Bootstrap to Moving Blocks for Time Series Regression Models," STICERD - Econometrics Paper Series 452, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    6. de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(5), pages 621-642, October.
    7. Chung, Ching-Fan & Baillie, Richard T, 1993. "Small Sample Bias in Conditional Sum-of-Squares Estimators of Fractionally Integrated ARMA Models," Empirical Economics, Springer, vol. 18(4), pages 791-806.
    8. Park, Joon Y., 2002. "An Invariance Principle For Sieve Bootstrap In Time Series," Econometric Theory, Cambridge University Press, vol. 18(2), pages 469-490, April.
    9. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
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    Citations

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    Cited by:

    1. George Kapetanios & Fotis Papailias, 2011. "Block Bootstrap and Long Memory," Working Papers 679, Queen Mary University of London, School of Economics and Finance.
    2. George Kapetanios & Fotis Papailias, 2011. "Block Bootstrap and Long Memory," Working Papers 679, Queen Mary University of London, School of Economics and Finance.
    3. Margherita Gerolimetto & Isabella Procidano, 2008. "A test for fractional cointegration using the sieve bootstrap," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(3), pages 373-391, July.

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    More about this item

    Keywords

    Long memory; Bootstrap;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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