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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

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  • Søren Johansen

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

Abstract

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

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    1. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), 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. 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.
    4. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    5. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    6. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    7. 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.
    8. Juselius, Katarina, 2006. "The Cointegrated VAR Model: Methodology and Applications," OUP Catalogue, Oxford University Press, number 9780199285679.
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    Cited by:

    1. Søren Johansen, 2010. "An Extension of Cointegration to Fractional Autoregressive Processes," Discussion Papers 10-28, University of Copenhagen. Department of Economics.
    2. Matthew T. Holt & Timo Teräsvirta, 2012. "Global Hemispheric Temperature Trends and Co–Shifting: A Shifting Mean Vector Autoregressive Analysis," CREATES Research Papers 2012-54, Department of Economics and Business Economics, Aarhus University.
    3. Laila Taskeen Qazi & Atta Ur Rahman & Saleem Gul, 2015. "Which Pairs of Stocks should we Trade? Selection of Pairs for Statistical Arbitrage and Pairs Trading in Karachi Stock Exchange," The Pakistan Development Review, Pakistan Institute of Development Economics, vol. 54(3), pages 215-244.
    4. Jean Chung & Guanchao Tong & Jiayou Chao & Wei Zhu, 2021. "Path Analysis of Sea-Level Rise and Its Impact," Stats, MDPI, vol. 5(1), pages 1-14, December.
    5. Holt, Matthew T. & Teräsvirta, Timo, 2020. "Global hemispheric temperatures and co-shifting: A vector shifting-mean autoregressive analysis," Journal of Econometrics, Elsevier, vol. 214(1), pages 198-215.

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    More about this item

    Keywords

    Regression correlation cointegration; model based inference; likelihood inference; annual mean temperature; sea level;
    All these keywords.

    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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