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Improved Prediction Limits For AR(p) and ARCH(p) Processes

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  • Paul Kabaila
  • Khreshna Syuhada

Abstract

. A new simulation‐based prediction limit that improves on any given estimative d‐step‐ahead prediction limit for a Markov process is described. This improved prediction limit can be found with almost no algebraic manipulations. Nonetheless, it has the same asymptotic coverage properties as the Barndorff‐Nielsen and Cox [Inference and Asymptotics (1994) Chapman and Hall, London] and Vidoni [Journal of Time Series Analysis Vol. 25, pp. 137–154.] (2004) improved prediction limits. The new simulation‐based prediction limit is ideally suited to those Markov process models for which the algebraic manipulations required for the latter improved prediction limits are very complicated. We illustrate the new method by applying it in the context of one‐step‐ahead prediction for a zero‐mean Gaussian AR(2) process and an ARCH(2) process.

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  • Paul Kabaila & Khreshna Syuhada, 2008. "Improved Prediction Limits For AR(p) and ARCH(p) Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 213-223, March.
    • Handle: RePEc:bla:jtsera:v:29:y:2008:i:2:p:213-223
    DOI: 10.1111/j.1467-9892.2007.00553.x
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    Cited by:

    1. Syuhada, Khreshna & Hakim, Arief & Suprijanto, Djoko & Muchtadi-Alamsyah, Intan & Arbi, Lukman, 2022. "Is Tether a safe haven of safe haven amid COVID-19? An assessment against Bitcoin and oil using improved measures of risk," Resources Policy, Elsevier, vol. 79(C).
    2. Eric Beutner & Alexander Heinemann & Stephan Smeekes, 2017. "A Justification of Conditional Confidence Intervals," Papers 1710.00643, arXiv.org, revised Jan 2019.
    3. Kabaila, Paul & Syuhada, Khreshna, 2010. "The asymptotic efficiency of improved prediction intervals," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1348-1353, September.
    4. Bony Josaphat & Khreshna Syuhada, 2020. "Dependent Conditional Value-at-Risk for Aggregate Risk Models," Papers 2009.02904, arXiv.org.

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