Improved Frequentist Prediction Intervals for Autoregressive Models by Simulation
Helske, J., & Nyblom, J. (2015). Improved Frequentist Prediction Intervals for Autoregressive Models by Simulation. In S. J. Koopman, & N. Shephard (Eds.), Unobserved Components and Time Series Econometrics (pp. 291-309). Oxford University Press.
Date
2015Discipline
TilastotiedeCopyright
© 2015 Oxford University Press. This is a final draft version of an article whose final and definitive form has been published by OUP. Published in this repository with the kind permission of the publisher.
It is well known that the so called plug-in prediction intervals for
autoregressive processes, with Gaussian disturbances, are too narrow,
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 what is 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
opens the path how to treat multi-step prediction intervals which are
obtained easily by simulation either directly from the posterior distribution
or using importance sampling. A notable improvement is
gained in frequentist coverage probabilities. An application of the
method to forecasting the annual gross domestic product growth in
the United Kingdom and Spain is given for the period 2002–2011 using
the estimation period 1962–2001.
...


Publisher
Oxford University PressIs part of publication
Unobserved Components and Time Series Econometrics, Ed. by S. J. Koopman, & N. Shephard. Oxford University Press, ISBN 978-0-19-968366-6Metadata
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