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A Simple Test for Spurious Regressions

  • Antonio E. Noriega
  • Daniel Ventosa-Santaulària

It has been found that the t-statistic for testing the null of no relationship between two independent variables diverges asymptotically under a wide variety of nonstationary data generating processes. This paper introduces a simple method which guarantees convergence of this t-statistic to a pivotal limit distribution, when there are drifts in the integrated processes generating the data, thus allowing asymptotic inference. This method can be used to distinguish a genuine relationship from a spurious one among integrated (I(1) and I(2)) processes. Simulation experiments show that the test has good properties in small samples. When applying the proposed procedure to real data (including the marriages and mortality data of Yule), we do not find (spurious) significant relationships between the variables.

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File URL: http://www.banxico.org.mx/publicaciones-y-discursos/publicaciones/documentos-de-investigacion/banxico/%7B38AD79EC-20F5-A90B-0AA0-6782C09DF785%7D.pdf
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Paper provided by Banco de México in its series Working Papers with number 2011-05.

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Date of creation: Aug 2011
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Handle: RePEc:bdm:wpaper:2011-05
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  1. Stewart, Chris, 2006. "Spurious correlation of I(0) regressors in models with an I(1) dependent variable," Economics Letters, Elsevier, vol. 91(2), pages 184-189, May.
  2. Ventosa-Santaulària, Daniel, 2008. "Spurious Regression," MPRA Paper 59008, University Library of Munich, Germany.
  3. Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers 8905, Michigan State - Econometrics and Economic Theory.
  4. Noriega, Antonio E. & Ventosa Santaulària, Daniel, 2005. "Spurious regression under broken trend stationarity," MPRA Paper 58768, University Library of Munich, Germany.
  5. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
  6. Uwe Hassler, 2003. "Nonsense regressions due to neglected time-varying means," Statistical Papers, Springer, vol. 44(2), pages 169-182, April.
  7. Serena Ng & Pierre Perron, 1997. "Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power," Boston College Working Papers in Economics 369, Boston College Department of Economics, revised 01 Sep 2000.
  8. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 2," Cowles Foundation Discussion Papers 819R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1987.
  9. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  10. Noriega, Antonio E. & Ventosa-Santaulària, Daniel, 2007. "Spurious Regression and Trending Variables," MPRA Paper 58775, University Library of Munich, Germany.
  11. Dickey, David A & Pantula, Sastry G, 1987. "Determining the Ordering of Differencing in Autoregressive Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 455-61, October.
  12. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
  13. Kim, Tae-Hwan & Lee, Young-Sook & Newbold, Paul, 2004. "Spurious regressions with stationary processes around linear trends," Economics Letters, Elsevier, vol. 83(2), pages 257-262, May.
  14. Hendry, David F. & Pagan, Adrian R. & Sargan, J.Denis, 1984. "Dynamic specification," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 18, pages 1023-1100 Elsevier.
  15. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers 0130, National Bureau of Economic Research, Inc.
  16. Nelson, Charles R & Kang, Heejoon, 1981. "Spurious Periodicity in Inappropriately Detrended Time Series," Econometrica, Econometric Society, vol. 49(3), pages 741-51, May.
  17. Michael C. Lovell, 2005. "A Simple Proof of the FWL (Frisch-Waugh-Lovell) Theorem," Wesleyan Economics Working Papers 2005-012, Wesleyan University, Department of Economics, revised Jan 2007.
  18. Marmol, Francesc, 1998. "Spurious regression theory with nonstationary fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 84(2), pages 233-250, June.
  19. Pantula, Sastry G., 1989. "Testing for Unit Roots in Time Series Data," Econometric Theory, Cambridge University Press, vol. 5(02), pages 256-271, August.
  20. Entorf, Horst, 1997. "Random walks with drifts: Nonsense regression and spurious fixed-effect estimation," Journal of Econometrics, Elsevier, vol. 80(2), pages 287-296, October.
  21. Pagan, Adrian, 1984. "Econometric Issues in the Analysis of Regressions with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 221-47, February.
  22. Tsay, Wen-Jen & Chung, Ching-Fan, 2000. "The spurious regression of fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 96(1), pages 155-182, May.
  23. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
  24. Sun, Yixiao, 2004. "A CONVERGENT t-STATISTIC IN SPURIOUS REGRESSIONS," Econometric Theory, Cambridge University Press, vol. 20(05), pages 943-962, October.
  25. Hassler, Uwe, 1996. "Spurious regressions when stationary regressors are included," Economics Letters, Elsevier, vol. 50(1), pages 25-31, January.
  26. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-56, September.
  27. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  28. Granger, Clive W.J. & Hyung, Namwon & Jeon, Yongil, 1998. "Spurious Regressions with Stationary Series," University of California at San Diego, Economics Working Paper Series qt7r3353t8, Department of Economics, UC San Diego.
  29. Marmol, Francesc, 1996. "Nonsense Regressions between Integrated Processes of Different Orders," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(3), pages 525-36, August.
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