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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.

Suggested Citation

  • Antonio E. Noriega & Daniel Ventosa-Santaulària, 2011. "A Simple Test for Spurious Regressions," Working Papers 2011-05, Banco de México.
  • Handle: RePEc:bdm:wpaper:2011-05
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    References listed on IDEAS

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    Keywords

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

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

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