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Polynomial Regressions and Nonsense Inference

Author

Listed:
  • Daniel Ventosa-Santaulària

    (Centro de Investigación y Docencia Económicas (CIDE), División de Economía, Carretera México-Toluca 3655 Col. Lomas de Santa Fe, Delegación Álvaro Obregón, México 01210, Mexico)

  • Carlos Vladimir Rodríguez-Caballero

    (Center for Research in Econometric Analysis of Time Series (CREATES) and Department of Economics and Business, Aarhus University, Fuglesangs Allé 4, Building 2622 (203), Aarhus V 8210, Denmark)

Abstract

Polynomial specifications are widely used, not only in applied economics, but also in epidemiology, physics, political analysis and psychology, just to mention a few examples. In many cases, the data employed to estimate such specifications are time series that may exhibit stochastic nonstationary behavior. We extend Phillips’ results (Phillips, P. Understanding spurious regressions in econometrics. J. Econom. 1986, 33, 311–340.) by proving that an inference drawn from polynomial specifications, under stochastic nonstationarity, is misleading unless the variables cointegrate. We use a generalized polynomial specification as a vehicle to study its asymptotic and finite-sample properties. Our results, therefore, lead to a call to be cautious whenever practitioners estimate polynomial regressions.

Suggested Citation

  • Daniel Ventosa-Santaulària & Carlos Vladimir Rodríguez-Caballero, 2013. "Polynomial Regressions and Nonsense Inference," Econometrics, MDPI, vol. 1(3), pages 1-13, November.
    • Handle: RePEc:gam:jecnmx:v:1:y:2013:i:3:p:236-248:d:30523
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    References listed on IDEAS

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    More about this item

    Keywords

    polynomial regression; misleading inference; integrated processes;
    All these keywords.

    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

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