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A bayesian analysis of trend determination in economic time series

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Author Info
Zivot Eric
C.B. Phillips Peter

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Abstract

In this paper we provide a comprehensive Bayesian posterior analysis of trend determination in general autoregressive models. Multiple lag autoregressive models with fitted drifts and time trends as well as models that allow for certain types of structural change in the deterministic components are considered. We utilize a modified information matrix-based prior that accommodates stochastic nonstationarity, takes into account the interactions between long-run and short-run dynamics and controls the degree of stochastic nonstationarity permitted. We derive analytic posterior densities for all of the trend determining parameters via the Laplace approximation to multivariate integrals. We also address the sampling properties of our posteriors under alternative data generating processes by simulation methods. We apply our Bayesian techniques to the Nelson-Plosser macroeconomic data and various stock price and dividend data. Contrary to DeJong and Whiteman (1989a,b,c), we do not find that the data overwhelmingly favor the existence of deterministic trends over stochastic trends. In addition, we find evidence supporting Perron's (1989) view that some of the Nelson and Plosser data are best construed as trend stationary with a change in the trend function occurring at 1929.

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File URL: http://www.informaworld.com/openurl?genre=article&doi=10.1080/07474939408800290&magic=repec&7C&7C8674ECAB8BB840C6AD35DC6213A474B5
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Publisher Info
Article provided by Taylor and Francis Journals in its journal Econometric Reviews.

Volume (Year): 13 (1994)
Issue (Month): 3 ()
Pages: 291-336
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Handle: RePEc:taf:emetrv:v:13:y:1994:i:3:p:291-336

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Related research
Keywords: Key Wordr And Phrases: Bayesian Analysis; Flat Prior; Fragile Inference; Hypergeometric Funaion; Ignorance Prior; Laplace Approximation; Structural Change; Unit Root;

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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.
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  2. 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!]
  3. 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!]
  4. Marsh, Terry A & Merton, Robert C, 1986. "Dividend Variability and Variance Bounds Tests for the Rationality ofStock Market Prices," American Economic Review, American Economic Association, vol. 76(3), pages 483-98, June. [Downloadable!] (restricted)
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  5. Rappoport, Peter & Reichlin, Lucrezia, 1989. "Segmented Trends and Non-stationary Time Series," Economic Journal, Royal Economic Society, vol. 99(395), pages 168-77, Supplemen. [Downloadable!] (restricted)
  6. Peter C.B. Phillips, 1990. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Cowles Foundation Discussion Papers 950, Cowles Foundation, Yale University. [Downloadable!]
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  7. Schotman, P. & Van Dijk, H.K., 1990. "A Bayesian Analysis Of The Unit Root In Real Exchange Rates," Papers 9015-a, Erasmus University of Rotterdam - Econometric Institute.
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  8. Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January. [Downloadable!] (restricted)
  9. Zivot, Eric & Andrews, Donald W K, 1992. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 251-70, July.
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  10. Holbert, Donald, 1982. "A Bayesian analysis of a switching linear model," Journal of Econometrics, Elsevier, vol. 19(1), pages 77-87, May. [Downloadable!] (restricted)
  11. Nathan S. Balke, 1991. "Modeling trends in macroeconomic time series," Economic and Financial Policy Review, Federal Reserve Bank of Dallas, issue May, pages 19-33.
  12. Lawrence J. Christiano, 1988. "Searching For a Break in GNP," NBER Working Papers 2695, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  13. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, vol. 71(3), pages 421-36, June. [Downloadable!] (restricted)
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  14. DeJong, David N, et al, 1992. "Integration versus Trend Stationarity in Time Series," Econometrica, Econometric Society, vol. 60(2), pages 423-33, March. [Downloadable!] (restricted)
  15. Perron, Pierre, 1988. "Trends and random walks in macroeconomic time series : Further evidence from a new approach," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 297-332. [Downloadable!] (restricted)
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  16. Sargan, John Denis & Bhargava, Alok, 1983. "Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk," Econometrica, Econometric Society, vol. 51(1), pages 153-74, January. [Downloadable!] (restricted)
  17. Schwert, G. William, 1987. "Effects of model specification on tests for unit roots in macroeconomic data," Journal of Monetary Economics, Elsevier, vol. 20(1), pages 73-103, July. [Downloadable!] (restricted)
  18. Balke, Nathan S. & Fomby, Thomas B., 1991. "Shifting trends, segmented trends, and infrequent permanent shocks," Journal of Monetary Economics, Elsevier, vol. 28(1), pages 61-85, August. [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. Peter C.B. Phillips, 1991. "Bayesian Routes and Unit Roots: de rebus prioribus semper est disputandum," Cowles Foundation Discussion Papers 986, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  2. Penelope Smith, 2006. "Bayesian Inference for a Threshold Autoregression with a Unit Root," Melbourne Institute Working Paper Series wp2006n20, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne. [Downloadable!]
  3. Maria-Helena A. Dias & Joilson Dias & Charles L. Evans, 2004. "Estimation Of The Cyclical Component Of Economic Time Series," Anais do XXXII Encontro Nacional de Economia [Proceedings of the 32th Brazilian Economics Meeting] 104, ANPEC - Associação Nacional dos Centros de Pósgraduação em Economia [Brazilian Association of Graduate Programs in Economics]. [Downloadable!]
  4. Pascalau, Razvan, 2008. "Unit Roots Tests with Smooth Breaks: An Application to the Nelson-Plosser Data Set," MPRA Paper 7220, University Library of Munich, Germany. [Downloadable!]
  5. 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!]
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  6. Peter C.B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Cowles Foundation Discussion Papers 1189, Cowles Foundation, Yale University. [Downloadable!]
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