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Trends versus Random Walks in Time Series Analysis


  • Durlauf, Steven N
  • Phillips, Peter C B


This paper studies the effects of spurious detrending in regression. The asymptotic behavior of traditional least squares estimators and tests are examined in the context of models where the generating mechanism is systematically misspecified by the presence of deterministic time trends. Most previous work on the subject has relied upon Monte Carlo studies to understand the issues involved in detrending data that is generated by integrated processes and our analytical results help to shed light on many of the simulation findings. Standard F tests and Hausman tests are shown to inadequately discriminate between the competing hypotheses. Durbin-Watson statistics, on the other hand, are shown to be valuable measures of series stationarity. The asymptotic properties of regressions and excess volatility tests with detrended integrated time series are also explored.
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  • Durlauf, Steven N & Phillips, Peter C B, 1988. "Trends versus Random Walks in Time Series Analysis," Econometrica, Econometric Society, vol. 56(6), pages 1333-1354, November.
  • Handle: RePEc:ecm:emetrp:v:56:y:1988:i:6:p:1333-54

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    References listed on IDEAS

    1. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
    2. Flavin, Marjorie A, 1983. "Excess Volatility in the Financial Markets: A Reassessment of the Empirical Evidence," Journal of Political Economy, University of Chicago Press, vol. 91(6), pages 929-956, December.
    3. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Oxford University Press, vol. 53(4), pages 473-495.
    4. Nelson, Charles R & Kang, Heejoon, 1981. "Spurious Periodicity in Inappropriately Detrended Time Series," Econometrica, Econometric Society, vol. 49(3), pages 741-751, May.
    5. Shiller, Robert J, 1979. "The Volatility of Long-Term Interest Rates and Expectations Models of the Term Structure," Journal of Political Economy, University of Chicago Press, vol. 87(6), pages 1190-1219, December.
    6. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    7. Sargan, John Denis & Bhargava, Alok, 1983. "Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk," Econometrica, Econometric Society, vol. 51(1), pages 153-174, January.
    8. Amemiya, Takeshi, 1973. "Generalized Least Squares with an Estimated Autocovariance Matrix," Econometrica, Econometric Society, vol. 41(4), pages 723-732, July.
    9. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    10. Hoffman, Dennis L. & Low, Stuart A. & Schlagenhauf, Don E., 1984. "Tests of rationality, neutrality and market efficiency : A Monte Carlo analysis of alternative test statistics," Journal of Monetary Economics, Elsevier, vol. 14(3), pages 339-363, November.
    11. Plosser, Charles I & Schwert, G William & White, Halbert, 1982. "Differencing as a Test of Specification," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(3), pages 535-552, October.
    12. Phillips, P. C. B. & Ouliaris, S., 1988. "Testing for cointegration using principal components methods," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 205-230.
    13. Gregory Mankiw, N. & Shapiro, Matthew D., 1985. "Trends, random walks, and tests of the permanent income hypothesis," Journal of Monetary Economics, Elsevier, vol. 16(2), pages 165-174, September.
    14. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    15. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    16. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-1056, September.
    17. 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.
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