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Confidence intervals with higher accuracy for short and long-memory linear processes

Author

Listed:
  • Masoud M. Nasari

    (School of Mathematics and Statistics
    Canadian Blood Services)

  • Mohamedou Ould-Haye

    (School of Mathematics and Statistics)

Abstract

In this paper an easy to implement method of stochastically weighing short and long-memory linear processes is introduced. The method renders asymptotically exact size confidence intervals for the population mean which are significantly more accurate than their classic counterparts for each fixed sample size n. It is illustrated both theoretically and numerically that the randomization framework of this paper produces randomized (asymptotic) pivotal quantities, for the mean, which admit central limit theorems with smaller magnitudes of error as compared to those of their leading classic counterparts. An Edgeworth expansion result for randomly weighted linear processes whose innovations do not necessarily satisfy the Cramer condition, is established. Numerical illustrations and applications to real world data are also included.

Suggested Citation

  • Masoud M. Nasari & Mohamedou Ould-Haye, 2022. "Confidence intervals with higher accuracy for short and long-memory linear processes," Statistical Papers, Springer, vol. 63(4), pages 1187-1220, August.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:4:d:10.1007_s00362-021-01265-w
    DOI: 10.1007/s00362-021-01265-w
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    References listed on IDEAS

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    5. Poskitt, D.S. & Grose, Simone D. & Martin, Gael M., 2015. "Higher-order improvements of the sieve bootstrap for fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 188(1), pages 94-110.
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