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Posterior Odds Testing for a Unit Root with Data-Based Model Selection

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Author Info
Peter C.B. Phillips () (Cowles Foundation, Yale University)
Werner Ploberger (Cowles Foundation, Yale University)

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Abstract

The Kalman filter is sued to derive updating equations for the Bayesian data density in discrete time linear regression models with stochastic regressors. The implied "Bayes model" has time varying parameters and conditionally heterogeneous error variances. A sigma-finite "Bayes model" measure is given and used to produce a new model selection criterion (PIC) and objective posterior odds tests for sharp null hypotheses like the presence of a unit root. Simulation results and an empirical application are reported. The simulations show that the new model selection criterion "PIC" works very well and is generally superior to the Schwarz criterion BIC even in stationary systems.

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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1017.

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Length: 35 pages
Date of creation: May 1992
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Publication status: Published in Econometric Theory (1994), 10: 774-808
Handle: RePEc:cwl:cwldpp:1017

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Kalman filter; Bayesian data density; stochastic regressors;

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Find related papers by JEL classification:
C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Bayesian Analysis
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing
C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications

References listed on IDEAS
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  1. Hannan, E. J., 1981. "Estimating the dimension of a linear system," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 459-473, December. [Downloadable!] (restricted)
  2. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 2," Cowles Foundation Discussion Papers 819R, Cowles Foundation, Yale University, revised Feb 1987. [Downloadable!]
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  3. Peter C.B. Phillips & Werner Ploberger, 1991. "Time Series Modelling with a Bayesian Frame of Reference: 1. Concepts and Illustrations," Cowles Foundation Discussion Papers 980, Cowles Foundation, Yale University. [Downloadable!]
  4. Phillips, Peter C. B., 1995. "Bayesian model selection and prediction with empirical applications," Journal of Econometrics, Elsevier, vol. 69(1), pages 289-331, September. [Downloadable!] (restricted)
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  5. Phillips, P C B, 1991. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 333-64, Oct.-Dec.. [Downloadable!] (restricted)
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