IDEAS home Printed from
   My bibliography  Save this article

Near Observational Equivalence and Theoretical size Problems with Unit Root Tests


  • Faust, Jon


Said and Dickey (1984, Biometrika 71, 599–608) and Phillips and Perron (1988, Biometrika 75, 335–346) have derived unit root tests that have asymptotic distributions free of nuisance parameters under very general maintained models. Under models as general as those assumed by these authors, the size of the unit root test procedures will converge to one, not the size under the asymptotic distribution. Solving this problem requires restricting attention to a model that is small, in a topological sense, relative to the original. Sufficient conditions for solving the asymptotic size problem yield some suggestions for improving finite-sample size performance of standard tests.

Suggested Citation

  • Faust, Jon, 1996. "Near Observational Equivalence and Theoretical size Problems with Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 12(04), pages 724-731, October.
  • Handle: RePEc:cup:etheor:v:12:y:1996:i:04:p:724-731_00

    Download full text from publisher

    File URL:
    File Function: link to article abstract page
    Download Restriction: no

    References listed on IDEAS

    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 183-206.
    3. Ruud, Paul A., 1991. "Extensions of estimation methods using the EM algorithm," Journal of Econometrics, Elsevier, vol. 49(3), pages 305-341, September.
    4. 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.
    5. Koop, Gary & Osiewalski, Jacek & Steel, Mark F J, 1994. "Bayesian Efficiency Analysis with a Flexible Form: The AIM Cost Function," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 339-346, July.
    6. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    7. Chib, Siddhartha, 1993. "Bayes regression with autoregressive errors : A Gibbs sampling approach," Journal of Econometrics, Elsevier, vol. 58(3), pages 275-294, August.
    8. Geweke, John & Keane, Michael P & Runkle, David, 1994. "Alternative Computational Approaches to Inference in the Multinomial Probit Model," The Review of Economics and Statistics, MIT Press, vol. 76(4), pages 609-632, November.
    9. repec:bla:restud:v:65:y:1998:i:3:p:361-93 is not listed on IDEAS
    10. Chib, Siddhartha & Greenberg, Edward, 1995. "Hierarchical analysis of SUR models with extensions to correlated serial errors and time-varying parameter models," Journal of Econometrics, Elsevier, vol. 68(2), pages 339-360, August.
    11. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", pages 125-132.
    12. McCulloch, Robert & Rossi, Peter E., 1994. "An exact likelihood analysis of the multinomial probit model," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 207-240.
    13. Koop, Gary, 1994. " Recent Progress in Applied Bayesian Econometrics," Journal of Economic Surveys, Wiley Blackwell, vol. 8(1), pages 1-34, March.
    14. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 19-40, Suppl. De.
    15. Albert, James H & Chib, Siddhartha, 1993. "Bayes Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 1-15, January.
    16. Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November.
    17. James Tobin, 1956. "Estimation of Relationships for Limited Dependent Variables," Cowles Foundation Discussion Papers 3R, Cowles Foundation for Research in Economics, Yale University.
    18. Chib, Siddhartha, 1992. "Bayes inference in the Tobit censored regression model," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 79-99.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. DUFOUR, Jean-Marie & JOUINI, Tarek, 2005. "Finite-Sample Simulation-Based Inference in VAR Models with Applications to Order Selection and Causality Testing," Cahiers de recherche 2005-12, Universite de Montreal, Departement de sciences economiques.
    2. Giovanni Forchini & Patrick Marsh, "undated". "Exact Inference for the Unit Root Hypothesis," Discussion Papers 00/54, Department of Economics, University of York.
    3. Christopher J. Neely & David E. Rapach, 2008. "Real interest rate persistence: evidence and implications," Review, Federal Reserve Bank of St. Louis, issue Nov, pages 609-642.
    4. Dufour, J.M., 2001. "Logique et tests d'hypotheses: reflexions sur les problemes mal poses en econometrie," Cahiers de recherche 2001-15, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    5. Engel, Charles, 2000. "Long-run PPP may not hold after all," Journal of International Economics, Elsevier, vol. 51(2), pages 243-273, August.
    6. Al-Zoubi, Haitham A., 2008. "The long swings in the spot exchange rates and the complex unit roots hypothesis," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 18(3), pages 236-244, July.
    7. St-Amant, P. & Tessier, D., 1998. "A Discussion of the Reliability of Results Obtained with Long-Run Identifying Restrictions," Staff Working Papers 98-4, Bank of Canada.
    8. Lucio Sarno & Mark P. Taylor, 2002. "Purchasing Power Parity and the Real Exchange Rate," IMF Staff Papers, Palgrave Macmillan, vol. 49(1), pages 1-5.
    9. Dufour, Jean-Marie, 2001. "Logique et tests d’hypothèses," L'Actualité Economique, Société Canadienne de Science Economique, vol. 77(2), pages 171-190, juin.
    10. Castro, Tomás del Barrio & Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2013. "The Impact Of Persistent Cycles On Zero Frequency Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 29(06), pages 1289-1313, December.
    11. Atsushi Inoue & Lutz Kilian, 2002. "Bootstrapping Autoregressive Processes with Possible Unit Roots," Econometrica, Econometric Society, vol. 70(1), pages 377-391, January.
    12. Pierre Perron & Eduardo Zorita & Iliyan Georgiev & Paulo M. M. Rodrigues & A. M. Robert Taylor, 2017. "Unit Root Tests and Heavy-Tailed Innovations," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(5), pages 733-768, September.
    13. Perron Pierre & Ren Linxia, 2011. "On the Irrelevance of Impossibility Theorems: The Case of the Long-run Variance," Journal of Time Series Econometrics, De Gruyter, pages 1-34.
    14. V. V. Chari & Patrick J. Kehoe & Ellen R. McGrattan, 2004. "A Critique of Structural VARs Using Real Business Cycle Theory," Levine's Bibliography 122247000000000518, UCLA Department of Economics.
    15. Sonali Das & Rangan Gupta & Patrick Kanda & Monique Reid & Christian Tipoy & Mulatu Zerihun, 2014. "Real interest rate persistence in South Africa: evidence and implications," Economic Change and Restructuring, Springer, vol. 47(1), pages 41-62, February.
    16. Zhijie Xiao & Luiz Renato Lima, 2007. "Testing Covariance Stationarity," Econometric Reviews, Taylor & Francis Journals, vol. 26(6), pages 643-667.
    17. Serena Ng & Pierre Perron, 2002. "PPP May not Hold Afterall: A Further Investigation," Annals of Economics and Finance, Society for AEF, vol. 3(1), pages 43-64, May.
    18. Paul Newbold & Tony Rayner & Neil Kellard, 2000. "Long-Run Drift, Co-Movement and Persistence in Real Wheat and Maize Prices," Journal of Agricultural Economics, Wiley Blackwell, vol. 51(1), pages 106-121.
    19. G. Forchini, 2005. "Some Properties of Tests for Possibly Unidentified Parameters," Monash Econometrics and Business Statistics Working Papers 21/05, Monash University, Department of Econometrics and Business Statistics.
    20. Xiao, Zhijie, 2012. "Robust inference in nonstationary time series models," Journal of Econometrics, Elsevier, vol. 169(2), pages 211-223.
    21. Newbold, Paul & Leybourne, Stephen & Wohar, Mark E., 2001. "Trend-stationarity, difference-stationarity, or neither: further diagnostic tests with an application to U.S. Real GNP, 1875-1993," Journal of Economics and Business, Elsevier, vol. 53(1), pages 85-102.
    22. Mehdi Hosseinkouchack & Uwe Hassler, 2016. "Powerful Unit Root Tests Free of Nuisance Parameters," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(4), pages 533-554, July.
    23. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2007. "A simple, robust and powerful test of the trend hypothesis," Journal of Econometrics, Elsevier, vol. 141(2), pages 1302-1330, December.
    24. Tsay, Wen-Jen, 2004. "Testing for contemporaneous correlation of disturbances in seemingly unrelated regressions with serial dependence," Economics Letters, Elsevier, vol. 83(1), pages 69-76, April.
    25. James Davidson & Dooruj Rambaccussing, 2015. "A test of the long memory hypothesis based on self-similarity," Dundee Discussion Papers in Economics 286, Economic Studies, University of Dundee.

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:12:y:1996:i:04:p:724-731_00. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Keith Waters). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.