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Near observational equivalence and unit root processes: formal concepts and implications

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  • Jon Faust

Abstract

A number of recent papers have discussed the fact that difference stationary and trend stationary processes are nearly observationally equivalent. The meaning of this fact, however, remains clouded. This paper defines near observational equivalence and derives several implications of the notion for classical and Bayesian unit root inference. For example, unless restrictions are imposed on the general difference and trend stationary models, the exact size of any consistent unit root test rises to one with sample size. Bayesian posteriors regarding unit roots are arbitrary in the sense that given any prior, there are other priors that agree with the first regarding empirical outcomes, but that imply arbitrarily different unit root posteriors.

Suggested Citation

  • Jon Faust, 1993. "Near observational equivalence and unit root processes: formal concepts and implications," International Finance Discussion Papers 447, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgif:447
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    References listed on IDEAS

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    1. John Y. Campbell & Pierre Perron, 1991. "Pitfalls and Opportunities: What Macroeconomists Should Know About Unit Roots," NBER Chapters,in: NBER Macroeconomics Annual 1991, Volume 6, pages 141-220 National Bureau of Economic Research, Inc.
    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..
    3. Christiano, Lawrence J. & Eichenbaum, Martin, 1990. "Unit roots in real GNP: Do we know, and do we care?," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 32(1), pages 7-61, January.
    4. Schwert, G William, 2002. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 5-17, January.
    5. Cochrane, John H., 1991. "A critique of the application of unit root tests," Journal of Economic Dynamics and Control, Elsevier, vol. 15(2), pages 275-284, April.
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    1. repec:nbp:nbpbik:v:47:y:2016:i:6:p:435-462 is not listed on IDEAS
    2. Christopher J. Neely & Lucio Sarno, 2002. "How well do monetary fundamentals forecast exchange rates?," Review, Federal Reserve Bank of St. Louis, issue Sep, pages 51-74.
    3. Rogers, John H., 1999. "Monetary shocks and real exchange rates," Journal of International Economics, Elsevier, vol. 49(2), pages 269-288, December.
    4. Campos, Julia & Ericsson, Neil R. & Hendry, David F., 1996. "Cointegration tests in the presence of structural breaks," Journal of Econometrics, Elsevier, vol. 70(1), pages 187-220, January.
    5. Marmol, Francesc & Reboredo, Juan C, 1999. " New Observational Equivalence and Fractionally Integrated Processes," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(2), pages 283-290, May.
    6. Nelson Mark, 1998. "Fundamentals of the Real Dollar-Pound Rate: 1871-1994," Working Papers 98-14, Ohio State University, Department of Economics.
    7. Chinn, Menzie D. & Meese, Richard A., 1995. "Banking on currency forecasts: How predictable is change in money?," Journal of International Economics, Elsevier, vol. 38(1-2), pages 161-178, February.
    8. Christopher J. Mayer & C. Tsuriel Somerville, 1996. "Unifying empirical and theoretical models of housing supply," Working Papers 96-12, Federal Reserve Bank of Boston.

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    Econometrics;

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