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Improved frequentist prediction intervals for autoregressive models by simulation
University of Jyväskylä, Jyväskylä, Finland.ORCID iD: 0000-0001-7130-793X
University of Jyväskylä, Jyväskylä, Finland.
2015 (English)In: Unobserved Components and Time Series Econometrics / [ed] Siem Jan Koopman and Neil Shephard, Oxford: Oxford University Press, 2015, p. 291-309Chapter in book (Other academic)
Abstract [en]

It is well known that the so-called plug-in prediction intervals for autoregressive processes, with Gaussian disturbances, are too short, i.e. the coverage probabilities fall below the nominal ones. However, simulation experiments show that the formulas borrowed from the ordinary linear regression theory yield one-step prediction intervals, which have coverage probabilities very close to that claimed. From a Bayesian point of view the resulting intervals are posterior predictive intervals when uniform priors are assumed for both autoregressive coefficients and logarithm of the disturbance variance. This finding enables one to see how to treat multi-step prediction intervals that are obtained by simulation either directly from the posterior distribution or using importance sampling. An application of the method to forecasting the annual gross domestic product growth in the United Kingdom and Spain is given for the period 2002 to 2011 using the estimation period 1962 to 2001.

Place, publisher, year, edition, pages
Oxford: Oxford University Press, 2015. p. 291-309
Keywords [en]
prediction interval, coverage probabilities, Bayesian estimation, multi-step forecasting, gross domestic product
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-144913DOI: 10.1093/acprof:oso/9780199683666.003.0013ISBN: 9780199683666 (print)ISBN: 9780191763298 (electronic)OAI: oai:DiVA.org:liu-144913DiVA, id: diva2:1180718
Available from: 2018-02-06 Created: 2018-02-06 Last updated: 2018-02-14Bibliographically approved

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Helske, Jouni

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
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  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf