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

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Abstract

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.

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Paper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 0203.

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Length: 21 pages
Date of creation: 29 May 2002
Date of revision:
Handle: RePEc:vic:vicewp:0203

Note: ISSN 1485-6441
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Keywords: Spurious regression; normality; homoskedasticity; asymptotic theory; unit roots;

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  1. Plosser, Charles I. & Schwert*, G. William, 1978. "Money, income, and sunspots: Measuring economic relationships and the effects of differencing," Journal of Monetary Economics, Elsevier, Elsevier, vol. 4(4), pages 637-660, November.
  2. Breusch, T S & Pagan, A R, 1980. "The Lagrange Multiplier Test and Its Applications to Model Specification in Econometrics," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 47(1), pages 239-53, January.
  3. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, Elsevier, vol. 33(3), pages 311-340, December.
  4. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, Elsevier, vol. 2(2), pages 111-120, July.
  5. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, Econometric Society, vol. 48(4), pages 817-38, May.
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