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Strong Approximation for Long Memory Processes with Applications

Author

Listed:
  • Qiying Wang

    (Australian National University)

  • Yan-Xia Lin

    (University of Wollongong)

  • Chandra M. Gulati

    (University of Wollongong)

Abstract

In this paper we inverstigate the strong approximation of a linear process with long memory to a Gaussian process. The results are then applied to derive the law of the iterated logarithm and Darling–Erdős type theorem for long memory processes under ideal conditions.

Suggested Citation

  • Qiying Wang & Yan-Xia Lin & Chandra M. Gulati, 2003. "Strong Approximation for Long Memory Processes with Applications," Journal of Theoretical Probability, Springer, vol. 16(2), pages 377-389, April.
    • Handle: RePEc:spr:jotpro:v:16:y:2003:i:2:d:10.1023_a:1023570510824
    DOI: 10.1023/A:1023570510824
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    References listed on IDEAS

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    1. Horvàth, Lajos & Shao, Qi-Man, 1996. "Darling-Erdos-type theorems for sums of Gaussian variables with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 63(1), pages 117-137, October.
    2. Hall, Peter, 1992. "Convergence rates in the central limit theorem for means of autoregressive and moving average sequences," Stochastic Processes and their Applications, Elsevier, vol. 43(1), pages 115-131, November.
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    Cited by:

    1. Qiying Wang & Peter C. B. Phillips, 2022. "A General Limit Theory for Nonlinear Functionals of Nonstationary Time Series," Cowles Foundation Discussion Papers 2337, Cowles Foundation for Research in Economics, Yale University.
    2. Eva Biswas & Farzad Sabzikar & Peter C. B. Phillips, 2022. "Boosting the HP Filter for Trending Time Series with Long Range Dependence," Cowles Foundation Discussion Papers 2347, Cowles Foundation for Research in Economics, Yale University.
    3. Florence Merlevède & Magda Peligrad, 2010. "Moderate Deviations for Linear Processes Generated by Martingale-Like Random Variables," Journal of Theoretical Probability, Springer, vol. 23(1), pages 277-300, March.

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