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Understanding Spurious Regressions in Econometrics

This paper provides an analytical study of spurious regressions involving the levels of economic time series. As asymptotic theory is developed for regressions that relate independent random walks. It is shown that the usual t ratio significance tests do not possess limiting distributions but actually diverge as the sample size T approaches infinity. The Durbin-Watson statistic, on the other hand, converges in probability to zero. An alternative asymptotic theory is also analyzed. An alternative asymptotic theory is developed based on the concept of continuous data recording. This theory together with the large sample asymptotics that we present go a long way towards explaining the experimental results of Granger and Newbold (1974, 1977).

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File URL: http://cowles.econ.yale.edu/P/cd/d07b/d0757.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 757.

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Length: 29 pages
Date of creation: Jul 1985
Date of revision:
Publication status: Published in Journal of Econometrics (1986), 33: 311-340
Handle: RePEc:cwl:cwldpp:757
Note: CFP 667.
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Phone: (203) 432-3702
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Web page: http://cowles.econ.yale.edu/

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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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  1. Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
  2. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
  3. Phillips, P. C. B., 1987. "Asymptotic Expansions in Nonstationary Vector Autoregressions," Econometric Theory, Cambridge University Press, vol. 3(01), pages 45-68, February.
  4. Plosser, Charles I. & Schwert*, G. William, 1978. "Money, income, and sunspots: Measuring economic relationships and the effects of differencing," Journal of Monetary Economics, Elsevier, vol. 4(4), pages 637-660, November.
  5. Phillips, P C B & Durlauf, S N, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Wiley Blackwell, vol. 53(4), pages 473-95, August.
  6. Bhargava, Alok, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Wiley Blackwell, vol. 53(3), pages 369-84, July.
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