IDEAS home Printed from
   My bibliography  Save this paper

The Autoregressive Conditional Root (ACR) Model


  • Frédérique Bec


  • Anders Rahbek


  • Neil Shephard



In this paper we propose and analyse the Autoregressive Conditional Root (ACR) timeseries model, which allows for endogenously generated regime switching between seemingly stationaryand non-stationary epochs. It proves to be an appealing alternative to existing nonlinear models suchas e.g. the threshold autoregressive or Markov switching classes of models, which are commonly used todescribe nonlinear dynamics as implied by arbitrage in presence of transaction costs. Simple conditionson the parameters of the ACR process and its innovations, are shown to imply geometric ergodicity,stationarity and existence of moments. Furthermore, we establish consistency and asymptotic normalityof the maximum likelihood estimators in the ACR model. An application to French-German exchangerate data illustrate the conclusions and analysis.

Suggested Citation

  • Frédérique Bec & Anders Rahbek & Neil Shephard, 2005. "The Autoregressive Conditional Root (ACR) Model," Working Papers 2005-26, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2005-26

    Download full text from publisher

    File URL:
    File Function: Crest working paper version
    Download Restriction: no

    References listed on IDEAS

    1. Duncan, Greg J & Holmlund, Bertil, 1983. "Was Adam Smith Right after All? Another Test of the Theory of Compensating Wage Differentials," Journal of Labor Economics, University of Chicago Press, vol. 1(4), pages 366-379, October.
    2. Peter Arcidiacono & John Bailey Jones, 2003. "Finite Mixture Distributions, Sequential Likelihood and the EM Algorithm," Econometrica, Econometric Society, vol. 71(3), pages 933-946, May.
    3. Ken Burdett & Melvyn Coles, 2003. "Equilibrium Wage-Tenure Contracts," Econometrica, Econometric Society, vol. 71(5), pages 1377-1404, September.
    4. Kevin Lang & Sumon Majumdar, 2004. "The Pricing Of Job Characteristics When Markets Do Not Clear: Theory And Policy Implications," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(4), pages 1111-1128, November.
    5. Bent Jesper Christensen & Rasmus Lentz & Dale T. Mortensen & George R. Neumann & Axel Werwatz, 2005. "On-the-Job Search and the Wage Distribution," Journal of Labor Economics, University of Chicago Press, vol. 23(1), pages 31-58, January.
    6. Jolivet, Gregory & Postel-Vinay, Fabien & Robin, Jean-Marc, 2006. "The empirical content of the job search model: Labor mobility and wage distributions in Europe and the US," European Economic Review, Elsevier, vol. 50(4), pages 877-907, May.
    7. Jos van Ommeren & Gerard J. van den Berg & Cees Gorter, 2000. "Estimating the Marginal Willingness to Pay for Commuting," Journal of Regional Science, Wiley Blackwell, vol. 40(3), pages 541-563.
    8. Kostiuk, Peter F, 1990. "Compensating Differentials for Shift Work," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages 1054-1075, October.
    9. Matthew S. Dey & Christopher J. Flinn, 2005. "An Equilibrium Model of Health Insurance Provision and Wage Determination," Econometrica, Econometric Society, vol. 73(2), pages 571-627, March.
    10. Fabien Postel-Vinay & Jean-Marc Robin, 2002. "Equilibrium Wage Dispersion with Worker and Employer Heterogeneity," Econometrica, Econometric Society, vol. 70(6), pages 2295-2350, November.
    11. Daniel, Christophe & Sofer, Catherine, 1998. "Bargaining, Compensating Wage Differentials, and Dualism of the Labor Market: Theory and Evidence for France," Journal of Labor Economics, University of Chicago Press, vol. 16(3), pages 546-575, July.
    12. Timothy J. Gronberg & W. Robert Reed, 1994. "Estimating Workers' Marginal Willingness to Pay for Job Attributes Using Duration Data," Journal of Human Resources, University of Wisconsin Press, vol. 29(3), pages 911-931.
    13. Herzog, Henry W, Jr & Schlottmann, Alan M, 1990. "Valuing Risk in the Workplace: Market Price, Willingness to Pay, and the Optimal Provision of Safety," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 463-470, August.
    14. Harald Dale-Olsen, 2006. "Estimating Workers' Marginal Willingness to Pay for Safety using Linked Employer-Employee Data," Economica, London School of Economics and Political Science, vol. 73(289), pages 99-127, February.
    15. Hwang, Hae-shin & Reed, W Robert & Hubbard, Carlton, 1992. "Compensating Wage Differentials and Unobserved Productivity," Journal of Political Economy, University of Chicago Press, vol. 100(4), pages 835-858, August.
    16. Geert Ridder & Gerard J. van den Berg, 2003. "Measuring Labor Market Frictions: A Cross-Country Comparison," Journal of the European Economic Association, MIT Press, vol. 1(1), pages 224-244, March.
    17. Rosen, Sherwin, 1974. "Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition," Journal of Political Economy, University of Chicago Press, vol. 82(1), pages 34-55, Jan.-Feb..
    18. Hwang, Hae-shin & Mortensen, Dale T & Reed, W Robert, 1998. "Hedonic Wages and Labor Market Search," Journal of Labor Economics, University of Chicago Press, vol. 16(4), pages 815-847, October.
    19. Charles Brown, 1980. "Equalizing Differences in the Labor Market," The Quarterly Journal of Economics, Oxford University Press, vol. 94(1), pages 113-134.
    20. Dey, Matthew & Flinn, Christopher, 2008. "Household search and health insurance coverage," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 43-63, July.
    21. Flinn, C. & Heckman, J., 1982. "New methods for analyzing structural models of labor force dynamics," Journal of Econometrics, Elsevier, vol. 18(1), pages 115-168, January.
    22. Goddeeris, John H, 1988. "Compensating Differentials and Self-selection: An Application to Lawyers," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 411-428, April.
    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. Bec, Frédérique & Zeng, Songlin, 2013. "Are Southeast Asian real exchange rates mean reverting?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 23(C), pages 265-282.
    2. Bec, Frederique & Guay, Alain & Guerre, Emmanuel, 2008. "Adaptive consistent unit-root tests based on autoregressive threshold model," Journal of Econometrics, Elsevier, vol. 142(1), pages 94-133, January.
    3. Adusei Jumah & Robert M. Kunst, 2016. "Optimizing time-series forecasts for inflation and interest rates using simulation and model averaging," Applied Economics, Taylor & Francis Journals, vol. 48(45), pages 4366-4378, September.

    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:crs:wpaper:2005-26. 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: (Sri Srikandan) or (Christopher F Baum). 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.