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Spurious regression under deterministic and stochastic trends

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  • Antonio E. Noriega

    ()
    (Department of Economics and Finance, Universidad de Guanajuato)

  • Daniel Ventosa-Santaularia

    ()
    (Department of Economics and Finance, Universidad de Guanajuato)

Abstract

This paper analyses the asymptotic and finite sample implications of a mixed nonstationary behavior among the dependent and explanatory variables in a linear spurious regression model. We study the cases when the nonstationarity in the dependent variable is deterministic (stochastic), while the nonstationarity in the explanatory variable is stochastic (deterministic). In particular, we derive the asymptotic distribution of statistics in a spurious regression equation when one variable follows a difference stationary process (a random walk with and without drift), while the other is characterized by deterministic nonstationarity (a linear trend model with and without structural breaks in the trend function). We find that the divergence rate is sensitive to the assumed mixture of nonstationarity in the data generating process, and the phenomenon of spurious regression itself, contrary to previous findings, depends on the presence of a linear trend in the regression equation. Simulation experiments and real data confirm our asymptotic results.

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Bibliographic Info

Paper provided by Universidad de Guanajuato, Department of Economics and Finance in its series Department of Economics and Finance Working Papers with number EM200503.

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Length: 16 pages
Date of creation: Jun 2005
Date of revision:
Publication status: Published in Oxford Bulletin of Economics and Statistics (2007)
Handle: RePEc:gua:wpaper:em200503

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Related research

Keywords: Unit roots; Trend stationarity; Structural breaks; Spurious regression;

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References

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  1. Daniel Ventosa-Santaularia & Antonio E. Noriega, 2005. "Spurious regression under broken trend stationarity," Computing in Economics and Finance 2005 186, Society for Computational Economics.
  2. 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.
  3. 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.
  4. 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.
  5. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
  6. Kormendi, Roger C & Meguire, Philip, 1990. "A Multicountry Characterization of the Nonstationarity of Aggregate Output," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 22(1), pages 77-93, February.
  7. Marmol, Francesc, 1998. "Spurious regression theory with nonstationary fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 84(2), pages 233-250, June.
  8. Perron, P., 1990. "Further Evidence On Breaking Trend Functions In Macroeconomics Variables," Papers 350, Princeton, Department of Economics - Econometric Research Program.
  9. 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.
  10. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119.
  11. 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.
  12. 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.
  13. 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.
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