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Spurious Regression Under Broken‐Trend Stationarity

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  • Antonio E. Noriega
  • Daniel Ventosa‐Santaulària

Abstract

. We study the phenomenon of spurious regression between two random variables, when the generating mechanism of individual series is assumed to follow a stationary process around a trend with (possibly) multiple breaks in the level and slope of trend. We develop the relevant asymptotic theory and show that the phenomenon of spurious regression occurs independent of the structure assumed for the errors. In contrast to previous findings, the presence of a spurious relationship will be less severe when breaks are present in the generating mechanism of individual series. This is true whether the regression model includes a linear trend or not. Simulations confirm our asymptotic results, and reveal that in finite samples, the phenomenon of spurious regression is sensitive to the presence of a linear trend in the regression model and to the relative location of breaks within the sample.

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  • Antonio E. Noriega & Daniel Ventosa‐Santaulària, 2006. "Spurious Regression Under Broken‐Trend Stationarity," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 671-684, September.
    • Handle: RePEc:bla:jtsera:v:27:y:2006:i:5:p:671-684
    DOI: 10.1111/j.1467-9892.2006.00482.x
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    as
    1. Noriega, Antonio E. & de Alba, Enrique, 2001. "Stationarity and structural breaks -- evidence from classical and Bayesian approaches," Economic Modelling, Elsevier, vol. 18(4), pages 503-524, December.
    2. 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.
    3. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
    4. Duck, N W, 1992. "UK Evidence on Breaking Trend Functions," Oxford Economic Papers, Oxford University Press, vol. 44(3), pages 426-439, July.
    5. repec:cup:etheor:v:13:y:1997:i:3:p:315-52 is not listed on IDEAS
    6. Clive Granger & Namwon Hyung & Yongil Jeon, 2001. "Spurious regressions with stationary series," Applied Economics, Taylor & Francis Journals, vol. 33(7), pages 899-904.
    7. Bai, Jushan, 1997. "Estimating Multiple Breaks One at a Time," Econometric Theory, Cambridge University Press, vol. 13(3), pages 315-352, June.
    8. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    9. Marmol, Francesc, 1996. "Correlation theory of spuriously related higher order integrated processes," Economics Letters, Elsevier, vol. 50(2), pages 169-173, February.
    10. Kejak, Michal, 2003. "Stages of growth in economic development," Journal of Economic Dynamics and Control, Elsevier, vol. 27(5), pages 771-800, March.
    11. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    12. Raj, Baldev, 1992. "International Evidence on Persistence in Output in the Presence of an Episodic Change," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(3), pages 281-293, July-Sept.
    13. Steven N. Durlauf, 1993. "Nonergodic Economic Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(2), pages 349-366.
    14. Bruce E. Hansen, 2001. "The New Econometrics of Structural Change: Dating Breaks in U.S. Labour Productivity," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 117-128, Fall.
    15. Clemente, Jesus & Montanes, Antonio & Reyes, Marcelo, 1998. "Testing for a unit root in variables with a double change in the mean," Economics Letters, Elsevier, vol. 59(2), pages 175-182, May.
    16. Cooper, Russell, 1994. "Equilibrium Selection in Imperfectly Competitive Economies with Multiple Equilibria," Economic Journal, Royal Economic Society, vol. 104(426), pages 1106-1122, September.
    17. Startz, Richard, 1998. "Growth States and Shocks," Journal of Economic Growth, Springer, vol. 3(3), pages 203-215, September.
    18. Marmol, Francesc, 1998. "Spurious regression theory with nonstationary fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 84(2), pages 233-250, June.
    19. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    20. 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.
    21. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    22. Acemoglu, Daron & Scott, Andrew, 1997. "Asymmetric business cycles: Theory and time-series evidence," Journal of Monetary Economics, Elsevier, vol. 40(3), pages 501-533, December.
    23. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119.
    24. Robin L. Lumsdaine & David H. Papell, 1997. "Multiple Trend Breaks And The Unit-Root Hypothesis," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 212-218, May.
    25. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    26. 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.
    27. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    28. Ben-David, Dan & Papell, David H., 1995. "The great wars, the great crash, and steady state growth: Some new evidence about an old stylized fact," Journal of Monetary Economics, Elsevier, vol. 36(3), pages 453-475, December.
    29. Francesc Marmol, 1995. "SPURIOUS REGRESSIONS BETWEEN I(d) PROCESSES," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(3), pages 313-321, May.
    30. Lau, Sau-Him Paul, 1997. "Using stochastic growth models to understand unit roots and breaking trends," Journal of Economic Dynamics and Control, Elsevier, vol. 21(10), pages 1645-1667, August.
    31. Ben-David, D. & Papell, D.H., 1995. "The Great War, The Great Crash and Steady State Growth: Some New Evidence an Old Stylized Fact," Papers 36-95, Tel Aviv - the Sackler Institute of Economic Studies.
    32. Zelhorst, Dick & de Haan, Jakob, 1995. "Testing for a Break in Output: New International Evidence," Oxford Economic Papers, Oxford University Press, vol. 47(2), pages 357-362, April.
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    Cited by:

    1. Noriega Antonio E. & Ventosa-Santaulària Daniel, 2006. "Spurious Regression and Econometric Trends," Working Papers 2006-05, Banco de México.
    2. Ventosa-Santaularària, Daniel & Gómez, Manuel, 2006. "Inflation and Breaks: the validity of the Dickey-Fuller test," MPRA Paper 58773, University Library of Munich, Germany.
    3. Gerdie Everaert & Hauke Vierke, 2016. "Demographics and Business Cycle Volatility: A Spurious Relationship?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(7), pages 1467-1477, November.
    4. H.D. Vinod, 2016. "New bootstrap inference for spurious regression problems," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(2), pages 317-335, February.
    5. Antonio E. Noriega & Daniel Ventosa-Santaularia, 2012. "The effect of structural breaks on the Engle-Granger test for cointegration," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 27(1), pages 99-132.
    6. Travaglini, Guido, 2008. "Dynamic GMM Estimation With Structural Breaks. An Application to Global Warming and its Causes," MPRA Paper 7108, University Library of Munich, Germany.
    7. Antonio E. Noriega & Daniel Ventosa‐Santaulària, 2007. "Spurious Regression and Trending Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 69(3), pages 439-444, June.
    8. Noriega Antonio E. & Ventosa-Santaulària Daniel, 2006. "Spurious Cointegration: The Engle-Granger Test in the Presence of Structural Breaks," Working Papers 2006-12, Banco de México.
    9. Daniel Ventosa-Santaularia, 2007. "Spurious Instrumental Variables," Department of Economics and Finance Working Papers EM200704, Universidad de Guanajuato, Department of Economics and Finance, revised Mar 2009.
    10. Antonio E. Noriega & Daniel Ventosa-Santaularia, 2005. "Spurious regression under deterministic and stochastic trends," Department of Economics and Finance Working Papers EM200503, Universidad de Guanajuato, Department of Economics and Finance.
    11. Noriega Antonio E. & Ventosa-Santaulària Daniel, 2010. "Spurious Long-Horizon Regression in Econometrics," Working Papers 2010-06, Banco de México.
    12. Travaglini, Guido, 2007. "The U.S. Dynamic Taylor Rule With Multiple Breaks, 1984-2001," MPRA Paper 3419, University Library of Munich, Germany, revised 15 Jun 2007.
    13. Hrishikesh D. Vinod, 2008. "Heteroscedasticity and Autocorrelation Efficient (HAE) Estimation and Pivots for Jointly Evolving Series," Fordham Economics Discussion Paper Series dp2008-15, Fordham University, Department of Economics.
    14. Noriega Antonio E. & Ventosa-Santaulària Daniel, 2011. "A Simple Test for Spurious Regressions," Working Papers 2011-05, Banco de México.
    15. Ventosa-Santaulària, Daniel & Noriega, Antonio E., 2015. "Long-run monetary neutrality under stochastic and deterministic trends," Economic Modelling, Elsevier, vol. 47(C), pages 372-382.
    16. Jin, Hao & Zhang, Jinsuo & Zhang, Si & Yu, Cong, 2013. "The spurious regression of AR(p) infinite-variance sequence in the presence of structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 25-40.
    17. Manuel Gómez Zaldivar & Oscar Manjarrez Castro & Daniel Ventosa-Santaulària, 2009. "Regresión espuria en especificaciones dinámicas," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(1), pages 1-20, May.
    18. Granger, Clive W.J., 2012. "Useful conclusions from surprising results," Journal of Econometrics, Elsevier, vol. 169(2), pages 142-146.
    19. Travaglini, Guido, 2010. "Dynamic Econometric Testing of Climate Change and of its Causes," MPRA Paper 23600, University Library of Munich, Germany.
    20. Ventosa-Santaulária, Daniel & Gómez-Zaldívar, Manuel, 2009. "Broken mean stationarity and the validity of the Dickey-Fuller test: the case of controlled inflation," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 29(1), May.

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    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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