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Polynomial Regressions and Nonsense Inference
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
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
* Author to whom correspondence should be addressed.
Received: 6 August 2013; in revised form: 28 October 2013 / Accepted: 7 November 2013 / Published: 18 November 2013
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
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Ventosa-Santaulària, D.; Rodríguez-Caballero, C.V. Polynomial Regressions and Nonsense Inference. Econometrics 2013, 1, 236-248.
Ventosa-Santaulària D, Rodríguez-Caballero CV. Polynomial Regressions and Nonsense Inference. Econometrics. 2013; 1(3):236-248.
Ventosa-Santaulària, Daniel; Rodríguez-Caballero, Carlos V. 2013. "Polynomial Regressions and Nonsense Inference." Econometrics 1, no. 3: 236-248.