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A Bayesian Analysis of Trend Determination in Economic Time Series

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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.

Suggested Citation

  • 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.
    • Handle: RePEc:cwl:cwldpp:1002
    Note: CFP 891.
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    References listed on IDEAS

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    1. 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.
    2. 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 333-364, Oct.-Dec..
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    6. 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.
    7. 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 483-498, June.
    8. Rappoport, Peter & Reichlin, Lucrezia, 1989. "Segmented Trends and Non-stationary Time Series," Economic Journal, Royal Economic Society, vol. 99(395), pages 168-177, Supplemen.
    9. 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.
    10. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    11. Holbert, Donald, 1982. "A Bayesian analysis of a switching linear model," Journal of Econometrics, Elsevier, vol. 19(1), pages 77-87, May.
    12. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    13. 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.
    14. 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.
    15. Banerjee, Anindya & Lumsdaine, Robin L & Stock, James H, 1992. "Recursive and Sequential Tests of the Unit-Root and Trend-Break Hypotheses: Theory and International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 271-287, July.
    16. 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.
    17. 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 421-436, June.
    18. DeJong, David N, et al, 1992. "Integration versus Trend Stationarity in Time Series," Econometrica, Econometric Society, vol. 60(2), pages 423-433, March.
    19. 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.
    20. 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.
    21. 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.
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    Cited by:

    1. 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.
    2. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
    3. Ruibing Qin & Zheng Tian & Hao Jin, 2011. "Truncating estimation for the change in stochastic trend with heavy-tailed innovations," Statistical Papers, Springer, vol. 52(1), pages 203-217, February.
    4. Hoek, Henk & Lucas, Andre & van Dijk, Herman K., 1995. "Classical and Bayesian aspects of robust unit root inference," Journal of Econometrics, Elsevier, vol. 69(1), pages 27-59, September.
    5. 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 32nd Brazilian Economics Meeting] 104, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    6. 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.
    7. Phillips, P C B, 1991. "Bayesian Routes and Unit Roots: De Rebus Prioribus Semper Est Disputandum," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 435-473, Oct.-Dec..
    8. Razvan Pascalau, 2010. "Unit root tests with smooth breaks: an application to the Nelson-Plosser data set," Applied Economics Letters, Taylor & Francis Journals, vol. 17(6), pages 565-570.

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    More about this item

    Keywords

    Autoregression; unit root; structural change;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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