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Asymptotic properties of sieve bootstrap prediction intervals for FARIMA processes

  • Rupasinghe, Maduka
  • Samaranayake, V.A.
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    The sieve bootstrap is a resampling technique that uses autoregressive approximations of order p to model invertible linear time series, where p is allowed to go to infinity with sample size n. The asymptotic properties of sieve bootstrap prediction intervals for stationary invertible linear processes with short memory have been established in the past. In this paper, we extend these results to long memory (FARIMA) processes. We show that under certain regularity conditions the sieve bootstrap provides consistent estimators of the conditional distribution of future values of FARIMA processes, given the observed data.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212002830
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    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 12 ()
    Pages: 2108-2114

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:12:p:2108-2114
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    1. Alonso, Andrés M. & Peña, Daniel & Romo, Juan, 2003. "On sieve bootstrap prediction intervals," Statistics & Probability Letters, Elsevier, vol. 65(1), pages 13-20, October.
    2. Bühlmann, Peter, 1995. "Moving-average representation of autoregressive approximations," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 331-342, December.
    3. 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.
    4. D. Poskitt, 2007. "Autoregressive approximation in nonstandard situations: the fractionally integrated and non-invertible cases," Annals of the Institute of Statistical Mathematics, Springer, vol. 59(4), pages 697-725, December.
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