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

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  • Phillips, Peter C.B.
  • Ploberger, Werner

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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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 10 (1994)
Issue (Month): 3-4 (August)
Pages: 774-808

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Handle: RePEc:cup:etheor:v:10:y:1994:i:3-4:p:774-808_00

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  1. Peter C.B. Phillips, 1990. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 950, Cowles Foundation for Research in Economics, Yale University.
  2. Phillips, Peter C. B., 1995. "Bayesian model selection and prediction with empirical applications," Journal of Econometrics, Elsevier, Elsevier, vol. 69(1), pages 289-331, September.
  3. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 1," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 811R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1987.
  4. Hannan, E. J., 1981. "Estimating the dimension of a linear system," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 11(4), pages 459-473, December.
  5. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 2," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 819R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1987.
  6. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, Elsevier, vol. 10(2), pages 139-162.
  7. Peter C.B. Phillips & Werner Ploberger, 1991. "Time Series Modelling with a Bayesian Frame of Reference: 1. Concepts and Illustrations," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 980, Cowles Foundation for Research in Economics, Yale University.
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