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Unit Root Testing Using Covariates: Some Theory and Evidence

Author

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  • Guglielmo Maria Caporale
  • Nikitas Pittis

Abstract

This paper analyzes the conditions under which power gains can be achieved using the Covariate Augmented Dickey‐Fuller test (CADF) rather than the conventional Augmented Dickey‐Fuller (ADF), and argues that this method has the advantage, relative to univariate unit root tests, of increasing power without suffering from the large size distortions affecting the latter. The inclusion of covariates affects unit root testing by: (a) reducing the standard error of the estimate of the autoregressive parameter without affecting the estimate itself, and/or (b) reducing both the standard error and the absolute value of the estimate itself. Conditions in terms of contemporaneous correlation and Granger causality are derived for case (a) or (b) to arise. As an illustration, it is shown that applying the more powerful CADF (rather than the ADF) test reverses the finding of a unit root for many US macroeconomic series.

Suggested Citation

  • Guglielmo Maria Caporale & Nikitas Pittis, 1999. "Unit Root Testing Using Covariates: Some Theory and Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(4), pages 583-595, November.
    • Handle: RePEc:bla:obuest:v:61:y:1999:i:4:p:583-595
    DOI: 10.1111/1468-0084.00145
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    Citations

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    Cited by:

    1. Lupi, Claudio, 2009. "Covariate Augmented Dickey-Fuller Tests with R," Economics & Statistics Discussion Papers esdp09051, University of Molise, Department of Economics.
    2. Elliott, Graham & Jansson, Michael, 2000. "Testing for Unit Roots with Stationary Covariances," Department of Economics, Working Paper Series qt47k7z69n, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    3. Mauro Costantini & Claudio Lupi, 2013. "A Simple Panel-CADF Test for Unit Roots," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 75(2), pages 276-296, April.
    4. Sebastian Fossati, 2013. "Unit root testing with stationary covariates and a structural break in the trend function," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(3), pages 368-384, May.
    5. Cláudia Duarte, 2015. "Covariate-augmented unit root tests with mixed-frequency data," Working Papers w201507, Banco de Portugal, Economics and Research Department.
    6. Aikins Abakah, Emmanuel Joel & Gil-Alana, Luis A. & Tripathy, Trilochan, 2022. "Stochastic structure of metal prices: Evidence from fractional integration non-linearities and breaks," Resources Policy, Elsevier, vol. 78(C).
    7. Elliott, Graham & Jansson, Michael, 2002. "Testing for Unit Roots with Stationary Covariates," Department of Economics, Working Paper Series qt4v35s2gv, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    8. Elliott, Graham & Jansson, Michael, 2002. "Testing for Unit Roots with Stationary Covariates," University of California at San Diego, Economics Working Paper Series qt4v35s2gv, Department of Economics, UC San Diego.
    9. Gil-Alana, Luis A. & Chang, Shinhye & Balcilar, Mehmet & Aye, Goodness C. & Gupta, Rangan, 2015. "Persistence of precious metal prices: A fractional integration approach with structural breaks," Resources Policy, Elsevier, vol. 44(C), pages 57-64.
    10. Paulo M.M. Rodrigues & Antonio Rubia, 2011. "A Class of Robust Tests in Augmented Predictive Regressions," Working Papers w201126, Banco de Portugal, Economics and Research Department.
    11. Lee, Cheng-Feng & Tsong, Ching-Chuan, 2009. "Bootstrapping covariate stationarity tests for inflation rates," Economic Modelling, Elsevier, vol. 26(6), pages 1443-1448, November.
    12. Elliott, Graham & Jansson, Michael, 2000. "Testing for Unit Roots with Stationary Covariances," University of California at San Diego, Economics Working Paper Series qt47k7z69n, Department of Economics, UC San Diego.
    13. Elliott, Graham & Jansson, Michael, 2003. "Testing for unit roots with stationary covariates," Journal of Econometrics, Elsevier, vol. 115(1), pages 75-89, July.
    14. Jomana Amara & David Papell, 2006. "Testing for Purchasing Power Parity using stationary covariates," Applied Financial Economics, Taylor & Francis Journals, vol. 16(1-2), pages 29-39.
    15. Costantini, Mauro & Lupi, Claudio & Popp, Stephan, 2007. "A Panel-CADF Test for Unit Roots," Economics & Statistics Discussion Papers esdp07039, University of Molise, Department of Economics.
    16. Siklos, Pierre L., 2010. "Meeting Maastricht: Nominal convergence of the new member states toward EMU," Economic Modelling, Elsevier, vol. 27(2), pages 507-515, March.
    17. Agosto, Arianna & Cerchiello, Paola & Pagnottoni, Paolo, 2022. "Sentiment, Google queries and explosivity in the cryptocurrency market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).

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