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The Joint Distribution of Forecast Errorsin the AR(1) Model

Published online by Cambridge University Press:  11 February 2009

Abstract

Second-order asymptotic expansion approximations to thejoint distributions of dynamic forecast errors andof static forecast errors in the stationary Gaussianpure AR(1) model are derived. The approximation tothe dynamic forecast errors distribution can beexpressed as a multivariate normal distribution withmodified mean vector and covariance matrix, thusgeneralizing the results of Phillips [12]. However,the approximation to the static forecast errorsdistribution includes skewness and kurtosis terms.Thus the class of multivariate normal distributionsdoes not provide as good approximations (in terms oferror convergence rates) to the distributions of thestatic forecast errors as to the distributions ofthe dynamic forecast errors. These results cast somedoubt on the appropriateness of model validationprocedures, such as Chow tests, which use the staticforecast errors and implicitly assume that thesehave a distribution which is well approximated by amultivariate normal.

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Type
Research Article
Copyright
Copyright © Cambridge University Press 1991

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