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The analysis of nonstationary time series using regression, correlation and cointegration with an application to annual mean temperature and sea level


  • Søren Johansen

    () (Department of Economics, University of Copenhagen and CREATES, University of Aarhus)


There are simple well-known conditions for the validity of regression and correlation as statistical tools. We analyse by examples the effect of nonstationarity on inference using these methods and compare them to model based inference. Finally we analyse some data on annual mean temperature and sea level, by applying the cointegrated vector autoregressive model, which explicitly takes into account the nonstationarity of the variables.

Suggested Citation

  • Søren Johansen, 2010. "The analysis of nonstationary time series using regression, correlation and cointegration with an application to annual mean temperature and sea level," CREATES Research Papers 2010-69, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2010-69

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    References listed on IDEAS

    1. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
    2. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    3. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    4. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    5. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    6. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    7. Juselius, Katarina, 2006. "The Cointegrated VAR Model: Methodology and Applications," OUP Catalogue, Oxford University Press, number 9780199285679.
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    More about this item


    Regression correlation cointegration; model based inference; likelihood inference; annual mean temperature; sea level;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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