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Parametric and Nonparametric Frequentist Model Selection and Model Averaging
Econometrics 2013, 1(3), 236-248; doi:10.3390/econometrics1030236
Article

Polynomial Regressions and Nonsense Inference

1,*  and 2
Received: 6 August 2013 / Revised: 28 October 2013 / Accepted: 7 November 2013 / Published: 18 November 2013
(This article belongs to the Special Issue Econometric Model Selection)
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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.
Keywords: polynomial regression; misleading inference; integrated processes polynomial regression; misleading inference; integrated processes
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Ventosa-Santaulària, D.; Rodríguez-Caballero, C.V. Polynomial Regressions and Nonsense Inference. Econometrics 2013, 1, 236-248.

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