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Correlation, Regression, and Cointegration of Nonstationary Economic Time Series

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  • Søren Johansen

    (Department of Economics, University of Copenhagen)

Abstract

Yule (1926) introduced the concept of spurious or nonsense correlation, and showed by simulation that for some nonstationary processes, that the empirical correlations seem not to converge in probability even if the processes were independent. This was later discussed by Granger and Newbold (1974), and Phillips (1986) found the limit distributions. We propose to distinguish between empirical and population correlation coefficients and show in a bivariate autoregressive model for nonstationary variables that the empirical correlation and regression coefficients do not converge to the relevant population values, due to the trending nature of the data. We conclude by giving a simple cointegration analysis of two interests. The analysis illustrates that much more insight can be gained about the dynamic behavior of the nonstationary variables then simply by calculating a correlation coefficient.

Suggested Citation

  • Søren Johansen, 2007. "Correlation, Regression, and Cointegration of Nonstationary Economic Time Series," Discussion Papers 07-25, University of Copenhagen. Department of Economics.
    • Handle: RePEc:kud:kuiedp:0725
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    References listed on IDEAS

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    1. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    2. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
    3. 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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    Cited by:

    1. Hultkrantz, Lars & A. Krüger, Niclas & Mantalos, Panagiotis, 2014. "Risk-adjusted long-term social rates of discount for transportation infrastructure investment," Research in Transportation Economics, Elsevier, vol. 47(C), pages 70-81.
    2. repec:zbw:rwirep:0435 is not listed on IDEAS
    3. Ansgar Belke & Marcel Wiedmann, 2013. "Monetary Policy, Stock Prices and Central Banks - Cross-Country Comparisons of Cointegrated VAR Models," Ruhr Economic Papers 0435, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    4. Ansgar Belke & Marcel Wiedmann, 2018. "Dissecting long-run and short-run causalities between monetary policy and stock prices," International Economics and Economic Policy, Springer, vol. 15(4), pages 761-786, October.
    5. Kathrin Goldmann, 2019. "Time-declining risk-adjusted social discount rates for transport infrastructure planning," Transportation, Springer, vol. 46(1), pages 17-34, February.
    6. Peter Schwendner & Martin Schuele & Thomas Ott & Martin Hillebrand, 2015. "European Government Bond Dynamics and Stability Policies: Taming Contagion Risks," Working Papers 8, European Stability Mechanism.
    7. Panagiotis Mantalos & Lars Hultkrantz, 2018. "Estimating ‘gamma’ for tail-hedge discount rates when project returns are cointegrated with GDP," Applied Economics, Taylor & Francis Journals, vol. 50(37), pages 4074-4085, August.
    8. Paul Alagidede & Theodore Panagiotidis & Xu Zhang, 2011. "Why a diversified portfolio should include African assets," Applied Economics Letters, Taylor & Francis Journals, vol. 18(14), pages 1333-1340.
    9. Fernández Macho, Francisco Javier, 2013. "A Note on Wavelet Correlation and Cointegration," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    10. Belke, Ansgar & Wiedmann, Marcel, 2013. "Monetary Policy, Stock Prices and Central Banks - Cross-Country Comparisons of Cointegrated VAR Models," Ruhr Economic Papers 435, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    11. Ansgar Belke & Marcel Wiedmann, 2013. "Money, Stock Prices and Central Banks – Cross-Country Comparisons of Cointegrated VAR Models," ROME Working Papers 201308, ROME Network.

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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