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

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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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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 986.

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

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Keywords: Bayesian analysis; time series;

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References

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  1. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
  2. Eric Zivot & Peter C.B. Phillips, 1991. "A Bayesian Analysis of Trend Determination in Economic Time Series," Cowles Foundation Discussion Papers 1002, Cowles Foundation for Research in Economics, Yale University.
  3. 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.
  4. Hiro Y. Toda & Peter C.B. Phillips, 1991. "Vector Autoregression and Causality," Cowles Foundation Discussion Papers 977, Cowles Foundation for Research in Economics, Yale University.
  5. 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.
  6. 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 for Research in Economics, Yale University.
  7. James H. Stock, 1991. "Confidence Intervals for the Largest Autoresgressive Root in U.S. Macroeconomic Time Series," NBER Technical Working Papers 0105, National Bureau of Economic Research, Inc.
  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. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  10. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  11. 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.
  12. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
  13. Peter C.B. Phillips, 1981. "Marginal Densities of Instrumental Variable Estimators in the General Single Equation Case," Cowles Foundation Discussion Papers 609, Cowles Foundation for Research in Economics, Yale University.
  14. 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.
  15. 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 for Research in Economics, Yale University.
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Citations

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Cited by:
  1. Monica Billio & Roberto Casarin & Francesco Ravazzolo & Herman K. van Dijk, 2012. "Combination schemes for turning point predictions," Working Paper 2012/04, Norges Bank.
  2. Kadane, Joseph B. & Chan, Ngai Hang & Wolfson, Lara J., 1996. "Priors for unit root models," Journal of Econometrics, Elsevier, vol. 75(1), pages 99-111, November.
  3. 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 for Research in Economics, Yale University.
  4. Yong Li & Jun Yu, 2010. "A New Bayesian Unit Root Test in Stochastic Volatility Models," Working Papers 21-2010, Singapore Management University, School of Economics, revised Oct 2010.
  5. Jin-Yu Zhang & Yong Li & Zhu-Ming Chen, 2013. "Unit Root Hypothesis in the Presence of Stochastic Volatility, a Bayesian Analysis," Computational Economics, Society for Computational Economics, vol. 41(1), pages 89-100, January.
  6. Ricardo Gonçalves Silva, 2004. "Bayesian Semiparametric Regression for Autoregressive Models with Possible Unit Roots," Econometrics 0405002, EconWPA.
  7. Peter C.B. Phillips, 1992. "Bayes Models and Forecasts of Australian Macroeconomic Time Series," Cowles Foundation Discussion Papers 1024, Cowles Foundation for Research in Economics, Yale University.
  8. 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 for Research in Economics, Yale University.
  9. Li, Yong & Chong, Terence Tai-Leung & Zhang, Jie, 2012. "Testing for a unit root in the presence of stochastic volatility and leverage effect," Economic Modelling, Elsevier, vol. 29(5), pages 2035-2038.
  10. Peter C.B. Phillips, 1991. "Unit Roots," Cowles Foundation Discussion Papers 998, Cowles Foundation for Research in Economics, Yale University.
  11. 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.
  12. N. Vijayamohanan Pillai, 2010. "Electricity Demand Analysis and Forecasting- The Tradition is Questioned," Working Papers id:2966, eSocialSciences.
  13. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2012. "Testing for unit roots in the presence of uncertainty over both the trend and initial condition," Journal of Econometrics, Elsevier, vol. 169(2), pages 188-195.
  14. Gael Martin, 2001. "Bayesian Analysis Of A Fractional Cointegration Model," Econometric Reviews, Taylor & Francis Journals, vol. 20(2), pages 217-234.
  15. Robert A. Amano & Simon van Norden, 1995. "Unit Root Tests and the Burden of Proof," Econometrics 9502005, EconWPA.

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