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On the Futility of Testing the Error Term Assumptions in a Spurious Regression



A spurious regression model is one in which the dependent and independent variables are non-stationary, but not cointegrated, and the data are not filtered (e.g., by differencing) before the model is estimated. It is well known that in this case the asymptotic behaviour of the least squares parameter estimates, their "t-ratios", the Durbin-Watson statistic and the R-squared, are all non-standard. In particular, the parameter estimates and R-squared converge weakly to functionals of standard Brownian motions; the "t-ratios" diverge in distribution; and the Durbin-Watson statistic converges in probability to zero. In this paper we show that similar results apply to other common tests of a spurious regression model's specification. In particular, standard tests of the Normality and homoskedasticity of the error term are doomed to always reject the null hypotheses, asymptotically. These results further reinforce the need to avoid the estimation of spurious regressions.

Suggested Citation

  • David E. A. Giles, 2002. "On the Futility of Testing the Error Term Assumptions in a Spurious Regression," Econometrics Working Papers 0203, Department of Economics, University of Victoria.
  • Handle: RePEc:vic:vicewp:0203 Note: ISSN 1485-6441

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    References listed on IDEAS

    1. 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.
    2. 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.
    3. T. S. Breusch & A. R. Pagan, 1980. "The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics," Review of Economic Studies, Oxford University Press, vol. 47(1), pages 239-253.
    4. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    5. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
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    More about this item


    Spurious regression; normality; homoskedasticity; asymptotic theory; unit roots;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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