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On the Shape of the Likelihood/Posterior in Cointegration Models

Published online by Cambridge University Press:  11 February 2009

Frank Kleibergen  and
Herman K. van Dijk
Frank Kleibergen
Affiliation:
Econometric Institute and Tinbergen Institüt
Herman K. van Dijk
Affiliation:
Erasmus University Rotterdam
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Abstract

A vector autoregressive (VAR) model is specified with equation system parameters, which directly reflect the possible cointegrating nature of the analyzed time series. By using a flat/diffuse prior, we show that the marginal posteriors of the parameters of interest (multipliers of the cointegrating vectors) may be nonintegrable and favor difference stationary models in an undesired way. To choose between stationary, cointegrated, and difference stationary models in a meaningful way, the Jeffreys prior principle is used. We investigate the sensitivity of the posterior results with respect to the construction of the Jeffreys prior. In this context, we also analyze the effect of fixed and stochastic initial values. The theoretical results are illustrated by using a VAR model for shortand long–term interest rates in the United States.

Type
Articles
Information
Econometric Theory , Volume 10 , Issue 3-4 , August 1994 , pp. 514 - 551
Copyright
Copyright © Cambridge University Press 1994

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