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A Simple Test for Spurious Regressions

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  • Antonio E. Noriega
  • Daniel Ventosa-Santaulària

Abstract

It has been 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. 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. 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 properties in small samples. When applying the proposed procedure to real data (including the marriages and mortality data of Yule), we do not find (spurious) significant relationships between the variables.

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File URL: http://www.banxico.org.mx/publicaciones-y-discursos/publicaciones/documentos-de-investigacion/banxico/%7B38AD79EC-20F5-A90B-0AA0-6782C09DF785%7D.pdf
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Paper provided by Banco de México in its series Working Papers with number 2011-05.

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Date of creation: Aug 2011
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Handle: RePEc:bdm:wpaper:2011-05

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Keywords: Spurious Regression; Integrated Process; Detrending; Asymptotic Theory; Cointegration; Monte Carlo Experiments.;

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  1. Antonio E. Noriega & Daniel Ventosa-Santaulària, 2006. "Spurious Regression Under Broken-Trend Stationarity," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 671-684, 09.
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