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Polynomial Regressions and Nonsense Inference

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Author(s): Daniel Ventosa-Santaulària | Carlos Vladimir Rodríguez-Caballero

Journal: Econometrics
ISSN 2225-1146

Volume: 1;
Issue: 3;
Start page: 236;
Date: 2013;
Original page

Keywords: polynomial regression | misleading inference | integrated processes

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.
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