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Bayesian Routes and Unit Roots: de rebus prioribus semper est disputandum

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

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Abstract

This paper provides detailed responses to the following 8 discussants of my paper "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends": Gary Koop and Mark Steel; Edward Leamer; In-Moo Kim and G.S. Maddala Dale J. Poirier; Peter C. Schotman and Herman K. van Dijk; James H. Stock; David Dejong and Charles H. Whiteman; and Christopher Sims. This reply puts new emphasis on the call made in the earlier paper for objective Bayesian analysis in time series; it underlines the need for a new approach, especially with regard to posterior odds testing; and it draws attention to a new methodology of Bayesian analysis developed in a recent paper by Phillips-Ploberger (1991). Some new simulations that shed light on certain comments of the discussants are proven; new empirical evidence is reported with the extended Nelson-Plosser data supplied by Schotman and van Dijk; and the new Phillips-Ploberger posterior odds test is given a brief empirical illustration.

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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 986.

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Length: 52 pages
Date of creation: Jul 1991
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Publication status: Published in Journal of Applied Econometrics (1991), 6: 435-473
Handle: RePEc:cwl:cwldpp:986

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

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Related research
Keywords: Bayesian analysis; time series;

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Find related papers by JEL classification:
C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Bayesian Analysis
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Phillips, P.C.B., 1986. "Testing for a Unit Root in Time Series Regression," Cahiers de recherche 8633, Universite de Montreal, Departement de sciences economiques.
    Other versions:
  2. Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, vol. 28(3), pages 435-459, December. [Downloadable!] (restricted)
    Other versions:
  3. Peter C.B. Phillips & Peter Schmidt, 1989. "Testing for a Unit Root in the Presence of Deterministic Trends," Cowles Foundation Discussion Papers 933, Cowles Foundation, Yale University. [Downloadable!]
  4. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January. [Downloadable!] (restricted)
  5. Peter C.B. Phillips, 1981. "Marginal Densities of Instrumental Variable Estimators in the General Single Equation Case," Cowles Foundation Discussion Papers 609, Cowles Foundation, Yale University. [Downloadable!]
  6. Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers 8905, Michigan State - Econometrics and Economic Theory.
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  7. Toda, Hiro Y & Phillips, Peter C B, 1993. "Vector Autoregressions and Causality," Econometrica, Econometric Society, vol. 61(6), pages 1367-93, November. [Downloadable!] (restricted)
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  8. Hendry, D.F. & Mizon, G.E., 1990. "Evaluating Dynamic Econometric Models By Encompassing The Var," Economics Series Working Papers 99102, University of Oxford, Department of Economics.
  9. Schwert, G William, 1989. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(2), pages 147-59, April.
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  10. 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!]
  11. Schotman, Peter & van Dijk, Herman K., 1991. "A Bayesian analysis of the unit root in real exchange rates," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 195-238. [Downloadable!] (restricted)
    Other versions:
  12. Eric Zivot & Peter C.B. Phillips, 1991. "A Bayesian Analysis of Trend Determination in Economic Time Series," Cowles Foundation Discussion Papers 1002, Cowles Foundation, Yale University. [Downloadable!]
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  13. Holly, A & Phillips, P C B, 1979. "A Saddlepoint Approximation to the Distribution of the k-Class Estimator of a Coefficient in a Simultaneous System," Econometrica, Econometric Society, vol. 47(6), pages 1527-47, November. [Downloadable!] (restricted)
  14. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-44, January. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Donald W.K. Andrews & Hong-Yuan Chen, 1992. "Approximately Median-Unbiased Estimation of Autoregressive Models with Applications to U.S. Macroeconomic and Financial Time Series," Cowles Foundation Discussion Papers 1026, Cowles Foundation, Yale University. [Downloadable!]
  2. Gael Martin, 2001. "Bayesian Analysis Of A Fractional Cointegration Model," Econometric Reviews, Taylor and Francis Journals, vol. 20(2), pages 217-234. [Downloadable!] (restricted)
  3. Peter C.B. Phillips, 1991. "Unit Roots," Cowles Foundation Discussion Papers 998, Cowles Foundation, Yale University. [Downloadable!]
  4. Peter C.B. Phillips, 1991. "The Long-Run Australian Consumption Function Reexamined: An Empirical Exercise in Bayesian Influence," Cowles Foundation Discussion Papers 1000, Cowles Foundation, Yale University. [Downloadable!]
  5. Peter C.B. Phillips, 1992. "Bayes Models and Forecasts of Australian Macroeconomic Time Series," Cowles Foundation Discussion Papers 1024, Cowles Foundation, Yale University. [Downloadable!]
  6. David I. Harvey & Stephen J. Leybourne & A. M. Robert Taylor, . "Testing for unit roots in the presence of uncertainty over both the trend and initial condition," Discussion Papers 08/03, University of Nottingham, Granger Centre for Time Series Econometrics. [Downloadable!]
  7. Gael M. Martin, 2000. "US deficit sustainability: a new approach based on multiple endogenous breaks," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(1), pages 83-105. [Downloadable!]
    Other versions:
  8. Ricardo Gonçalves Silva, 2004. "Bayesian Semiparametric Regression for Autoregressive Models with Possible Unit Roots," Econometrics 0405002, EconWPA. [Downloadable!]
  9. Robert A. Amano & Simon van Norden, 1995. "Unit Root Tests and the Burden of Proof," Econometrics 9502005, EconWPA. [Downloadable!]
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