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).
|Date of creation:||Jul 1985|
|Date of revision:|
|Publication status:||Published in Journal of Econometrics (1986), 33: 311-340|
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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
- Phillips, P. C. B., 1987.
"Asymptotic Expansions in Nonstationary Vector Autoregressions,"
Cambridge University Press, vol. 3(01), pages 45-68, February.
- Peter C.B. Phillips, 1985. "Asymptotic Expansions in Nonstationary Vector Autoregressions," Cowles Foundation Discussion Papers 765, Cowles Foundation for Research in Economics, Yale University.
- 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.
- 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.
- Peter C.B. Phillips & Steven N. Durlauf, 1985. "Multiple Time Series Regression with Integrated Processes," Cowles Foundation Discussion Papers 768, Cowles Foundation for Research in Economics, Yale University.
- 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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