Spurious Regression and Trending Variables*
| Published date | 01 June 2007 |
| Author | Daniel Ventosa‐Santaulària,Antonio E. Noriega |
| DOI | http://doi.org/10.1111/j.1468-0084.2007.00481.x |
| Date | 01 June 2007 |
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©Blackwell Publishing Ltd and the Department of Economics, University of Oxford, 2007. Published by Blackwell Publishing Ltd,
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OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 69, 3 (2007) 0305-9049
doi: 10.1111/j.1468-0084.2007.00481.x
Spurious Regression and Trending Variables*
Antonio E. Noriega† and Daniel Ventosa-Santaul `
aria‡
†Escuela de Economía, Universidad de Guanajuato, Guanajuato, and Dirección General de
Investigación Económica, Banco de México, D.F., México
(e-mail: anoriega@banxico.org.mx)
‡Escuela de Economía, Universidad de Guanajuato, Guanajuato, México
(e-mail: daniel@ventosa-santaularia.com)
Abstract
This paper analyses the asymptotic and finite-sample implications of different types
of non-stationary behaviour among the dependent and explanatory variables in a linear
spurious regression model. We study cases when the non-stationarity in the depen-
dent and explanatory variables is deterministic as well as stochastic. In particular,
we derive the order in probability of the t-statistic in a spurious regression equation
under a variety of empirically relevant data generation processes, and show that
the spurious regression phenomenon is present in all cases when both dependent
and explanatory variables behave in a non-stationary way. Simulation experiments
confirm our asymptotic results.
I. Introduction
It has been documented in recent studies that the phenomenon of spurious regres-
sion is present under different forms of non-stationarity in the data-generating process
(DGP). 1In particular, when the variables ytand xtare non-stationary and independent
of each other, ordinary least squares (OLS) applied to the regression model
*We would like to thank an anonymous referee for very helpful comments. We would also like to thank
Carlos Capistr´an, Daniel Chiquiar and seminar participants at Banco de M´exico, ITAM, the Computing in
Economics and Finance conference in Cyprus, the Time Series Econometrics, Finance and Risk conference
in Australia, and the Conference on Stochastic Processes and theirApplications in Paris. The opinions in this
paper correspond to the authors and do not necessarily reflect the point of view of Banco de M´exico.
JEL Classification numbers: C12, C13, C22.
1See Granger and Newbold (1974), Phillips (1986), Marmol (1995, 1996, 1998), Hassler (1996, 2000, 2003),
Entorf (1997), Cappuccio and Lubian (1997), Granger, Hyung and Jeon (1998), Kim, Lee and Newbold (2004)
(KLN henceforth), and Noriega and Ventosa-Santaul`aria (2006) (NVS hereafter).
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