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A Bayesian Analysis Of The Unit Root Hypothesis Within An Unobserved Components Model

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  • Zivot, Eric

Abstract

In this paper we extend some of Phillips's [4] results to nonlinear unobserved components models and develop a posterior odds ratio test of the unit root hypothesis based on flat and Jeffreys priors. In contrast to the analysis presented by Schotman and van Dijk [9], we utilize a nondegenerate structural representation of the components model that allows us to determine well-behaved Jeffreys priors, posterior densities under flat priors and Jeffreys priors, and posterior odds ratios for the unit root hypothesis without a proper prior for the level parameter. The analysis highlights the importance of the treatment of initial values for inference concerning stationarity and unit roots.

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  • Zivot, Eric, 1994. "A Bayesian Analysis Of The Unit Root Hypothesis Within An Unobserved Components Model," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 552-578, August.
    • Handle: RePEc:cup:etheor:v:10:y:1994:i:3-4:p:552-578_00
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    1. Månsson, Kristofer & Shukur, Ghazi & Sjölander, Pär, 2012. "Testing for Panel Cointegration in an Error Correction Framework - with an Application to the Fisher Hypothesis," HUI Working Papers 72, HUI Research.
    2. Richard Kleijn & Herman K. van Dijk, 2006. "Bayes model averaging of cyclical decompositions in economic time series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(2), pages 191-212.
    3. Cribari-Neto, Francisco, 1996. "On time series econometrics," The Quarterly Review of Economics and Finance, Elsevier, vol. 36(Supplemen), pages 37-60.
    4. Paap, Richard & van Dijk, Herman K, 2003. "Bayes Estimates of Markov Trends in Possibly Cointegrated Series: An Application to U.S. Consumption and Income," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 547-563, October.
    5. Alessandro Calza & Andrea Zaghini, 2010. "Sectoral Money Demand and the Great Disinflation in the United States," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(8), pages 1663-1678, December.
    6. Magris Martin & Iosifidis Alexandros, 2021. "Approximate Bayes factors for unit root testing," Papers 2102.10048, arXiv.org, revised Feb 2021.
    7. Kim, Chang-Jin & Nelson, Charles R, 2001. "A Bayesian Approach to Testing for Markov-Switching in Univariate and Dynamic Factor Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(4), pages 989-1013, November.
    8. Pere, Pekka, 2000. "Adjusted estimates and Wald statistics for the AR(1) model with constant," Journal of Econometrics, Elsevier, vol. 98(2), pages 335-363, October.
    9. Kleijn, R.H. & van Dijk, H.K., 2001. "A Bayesian analysis of the PPP puzzle using an unobserved components model," Econometric Institute Research Papers EI 2001-35, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    10. Charley Xia and William Griffiths, 2012. "Bayesian Unit Root Testing: The Effect Of Choice Of Prior On Test Outcomes," Department of Economics - Working Papers Series 1152, The University of Melbourne.
    11. Marriott, John & Newbold, Paul, 2000. "The strength of evidence for unit autoregressive roots and structural breaks: A Bayesian perspective," Journal of Econometrics, Elsevier, vol. 98(1), pages 1-25, September.
    12. Carter Richard A. L. & Zellner Arnold, 2004. "The ARAR Error Model for Univariate Time Series and Distributed Lag," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(1), pages 1-44, March.
    13. Loukia Meligkotsidou & Elias Tzavalis & Ioannis D. Vrontos, 2012. "A Bayesian panel data framework for examining the economic growth convergence hypothesis: do the G7 countries converge?," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(9), pages 1975-1990, May.
    14. Triantafyllopoulos, K. & Nason, G.P., 2007. "A Bayesian analysis of moving average processes with time-varying parameters," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 1025-1046, October.
    15. Meligkotsidou, Loukia & Tzavalis, Elias & Vrontos, Ioannis, 2017. "On Bayesian analysis and unit root testing for autoregressive models in the presence of multiple structural breaks," Econometrics and Statistics, Elsevier, vol. 4(C), pages 70-90.
    16. Kociecki, Andrzej, 2012. "Orbital Priors for Time-Series Models," MPRA Paper 42804, University Library of Munich, Germany.

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