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A simple solution of the spurious regression problem

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  • Wang, Cindy Shin-Huei
  • Hafner, Christian

Abstract

This paper develops a new estimator for cointegrating and spurious regressions by applying a two-stage generalized Cochrane-Orcutt transformation based on an autoregressive approximation framework, even though the exact form of the error term is unknown in practice. We prove that our estimator is consistent for a wide class of regressions. We further show that a convergent usual t-statistic based on our new estimator can be constructed for the spurious regression cases analyzed by (Granger, C. W. J., and P. Newbold. 1974. “Spurious Regressions in Econometrics.” Journal of Econometrics 74: 111–120) and (Granger, C. W. J., N. Hyung, and H. Jeon. 2001. “Spurious Regressions with Stationary Series.” Applied Economics 33: 899–904). The implementation of our estimator is easy since it does not necessitate estimation of the long-run variance. Simulation results indicate the good statistical properties of the new estimator in small and medium samples, and also consider a more general framework including multiple regressors and endogeneity.
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Suggested Citation

  • Wang, Cindy Shin-Huei & Hafner, Christian, 2018. "A simple solution of the spurious regression problem," LIDAM Reprints ISBA 2018044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2018044
    Note: In : Studies in Nonlinear Dynamics & Econometrics, vol. 22, no. 3, p. 1-14 (2018)
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    1. Bauer, Dietmar & Wagner, Martin, 2005. "Autoregressive Approximations of Multiple Frequency I(1) Processes," Economics Series 174, Institute for Advanced Studies.
    2. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    3. Choi, Chi-Young & Hu, Ling & Ogaki, Masao, 2008. "Robust estimation for structural spurious regressions and a Hausman-type cointegration test," Journal of Econometrics, Elsevier, vol. 142(1), pages 327-351, January.
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    5. Ai Deng, 2014. "Understanding Spurious Regression in Financial Economics," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 122-150.
    6. Valkanov, Rossen, 2003. "Long-horizon regressions: theoretical results and applications," Journal of Financial Economics, Elsevier, vol. 68(2), pages 201-232, May.
    7. Haldrup, Niels, 1994. "The asymptotics of single-equation cointegration regressions with I(1) and I(2) variables," Journal of Econometrics, Elsevier, vol. 63(1), pages 153-181, July.
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    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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