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Priors For The Ar(1) Model: Parameterization Issues and Time Series Considerations

Published online by Cambridge University Press:  11 February 2009

Peter C. Schotman
Peter C. Schotman
Affiliation:
University of Limburg
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Abstract

Two issues have come up in the specification of a prior in the Bayesian analysis of time series with possible unit roots. The first issue deals with the singularity that is due to the local identification problem of the unconditional mean of an AR(1) process in the limit of a random walk. This singularity problem is related to the difference between a structural parameterization and the linear reduced form in a standard regression model with fixed regressors. The second is related to the time series nature of the regressor in an AR(1) model. In this paper we will concentrate on the parameterization issue. First, it is shown that the posterior of the autoregressive parameter can be very sensitive to the degree of prior dependence between the unconditional mean and the autocorrelation parameter. Second, the time series nature of the problem suggests a particular form of this dependence.

Type
Articles
Information
Econometric Theory , Volume 10 , Issue 3-4 , August 1994 , pp. 579 - 595
Copyright
Copyright © Cambridge University Press 1994

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