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On the Definitions of (Co-)Integration

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  • Karim M. Abadir
  • A. M. Robert Taylor

Abstract

Two problems exist in testing for (co‐)integration. One is that current definitions of fractional integration in the time domain can be incomplete. The other is that disregarding fractional orders of integration can cause incorrectly sized inference about cointegration. This paper completes the time‐domain definition of fractional integration, and defines cointegration in a general setting. As a by‐product of the latter, testing for cointegration in models without a pre‐specified functional form is shown to avoid a common inferential problem. Finally, we analyse the effects of using incomplete definitions of integration and/or cointegration. For the latter, incomplete I(1)‐null procedures make cointegration seem more likely than it actually is, while incomplete I(0)‐null procedures reject cointegration too often.
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  • Karim M. Abadir & A. M. Robert Taylor, "undated". "On the Definitions of (Co-)Integration," Discussion Papers 97/19, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:97/19
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    Cited by:

    1. BADALYAN, Gohar & HERZFELD, Thomas & RAJCANIOVA, Miroslava, 2014. "Transport Infrastructure And Economic Growth: Panel Data Approach For Armenia, Georgia And Turkey," Review of Agricultural and Applied Economics (RAAE), Faculty of Economics and Management, Slovak Agricultural University in Nitra, vol. 17(2), pages 1-10, October.
    2. Brunetti, Celso & Gilbert, Christopher L., 2000. "Bivariate FIGARCH and fractional cointegration," Journal of Empirical Finance, Elsevier, vol. 7(5), pages 509-530, December.
    3. Karim M. Abadir & Gabriel Talmain, 2012. "Beyond Co-Integration: Modelling Co-Movements in Macro finance," Working Paper series 25_12, Rimini Centre for Economic Analysis.
    4. Frank S. Nielsen, 2008. "Local polynomial Whittle estimation covering non-stationary fractional processes," CREATES Research Papers 2008-28, Department of Economics and Business Economics, Aarhus University.
    5. Giovanni Caggiano & Leone Leonida, 2009. "International output convergence: evidence from an autocorrelation function approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(1), pages 139-162.
    6. Karim M. Abadir & Gabriel Talmain, 2008. "Macro and Financial Markets: The Memory of an Elephant?," Working Paper series 17_08, Rimini Centre for Economic Analysis.
    7. Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, vol. 106(2), pages 217-241, February.
    8. Aaron Smallwood & Stefan Norrbin, 2004. "Estimating cointegrating vectors using near unit root variables," Applied Economics Letters, Taylor & Francis Journals, vol. 11(12), pages 781-784.
    9. Hélène Chevrou-Séverac, 2002. "Convergence monétaire européenne, PPA et PINC," Économie et Prévision, Programme National Persée, vol. 155(4), pages 79-94.
    10. Emma Iglesias & Garry Phillips, 2005. "Analysing one-month Euro-market interest rates by fractionally integrated models," Applied Financial Economics, Taylor & Francis Journals, vol. 15(2), pages 95-106.
    11. Karim Maher Abadir, 2004. "Cointegration Theory, Equilibrium and Disequilibrium Economics," Manchester School, University of Manchester, vol. 72(1), pages 60-71, January.
    12. Robert M. Kunst & Michael Reutter, 2000. "Decisions on Seasonal Unit Roots," CESifo Working Paper Series 286, CESifo.
    13. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2009. "Two estimators of the long-run variance: Beyond short memory," Journal of Econometrics, Elsevier, vol. 150(1), pages 56-70, May.
    14. Abadir, Karim & Talmain, Gabriel, 2005. "Distilling co-movements from persistent macro and financial series," Working Paper Series 525, European Central Bank.

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