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A Simple Test for Spurious Regressions

Listed author(s):
  • Antonio E. Noriega

    ()

    (Dirección General de Investigación Económica, Banco de México and Departamento de Department of Economics and Finance, Universidad de Guanajuato)

  • Daniel Ventosa-Santaularia

    ()

    (Department of Economics and Finance, Universidad de Guanajuato)

The literature on spurious regressions has found that the t-statistic for testing the null of no relationship between two independent variables diverges asymptotically under a wide variety of nonstationary data generating processes for the dependent and explanatory variables. This paper introduces a simple method which guarantees convergence of this t-statistic to a pivotal limit distribution, when there are drifts in the integrated processes generating the data, thus allowing asymptotic inference. We show that this method can be used to distinguish a genuine relationship from a spurious one among integrated (I(1) and I(2)) processes. Simulation experiments show that the test has good size and power properties in small samples. We apply the proposed procedure to several pairs of apparently independent integrated variables (including the marriages and mortality data of Yule, 1926), and find that our procedure, in contrast to standard ordinary least squares regression, does not find (spurious) significant relationships between the variables.

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File URL: ftp://ftp.econ.au.dk/creates/rp/11/rp11_15.pdf
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Paper provided by Department of Economics and Business Economics, Aarhus University in its series CREATES Research Papers with number 2011-15.

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Length: 25
Date of creation: 01 May 2011
Handle: RePEc:aah:create:2011-15
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  26. PERRON, Pierre & RODRIGUEZ, Gabriel, 1998. "GLS Detrending, Efficient Unit Root Tests and Structural Change," Cahiers de recherche 9809, Universite de Montreal, Departement de sciences economiques.
  27. Michael C. Lovell, 2005. "A Simple Proof of the FWL (Frisch-Waugh-Lovell) Theorem," Wesleyan Economics Working Papers 2005-012, Wesleyan University, Department of Economics, revised Jan 2007.
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