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Asymptotic properties of sieve bootstrap prediction intervals for FARIMA processes

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  • Rupasinghe, Maduka
  • Samaranayake, V.A.

Abstract

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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  • 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.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:12:p:2108-2114
    DOI: 10.1016/j.spl.2012.07.011
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    1. 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, March.
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    4. Bühlmann, Peter, 1995. "Moving-average representation of autoregressive approximations," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 331-342, December.
    5. Alonso, Andrés M. & Peña, Daniel & Romo, Juan, 2003. "On sieve bootstrap prediction intervals," Statistics & Probability Letters, Elsevier, vol. 65(1), pages 13-20, October.
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    Cited by:

    1. Veiga, Helena, 2015. "Model uncertainty and the forecast accuracy of ARMA models: A survey," DES - Working Papers. Statistics and Econometrics. WS ws1508, Universidad Carlos III de Madrid. Departamento de Estadística.

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