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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

    () (University of Copenhagen)

Abstract

There are simple well-known conditions for the validity of regression and correlation as statistical tools. We analyse by examples the e¤ect 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, 2011. "The analysis of nonstationary time series using regression, correlation and cointegration - with an application to annual mean temperature and sea level," DSS Empirical Economics and Econometrics Working Papers Series 2011/4, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.
  • Handle: RePEc:sas:wpaper:20114
    as

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    File URL: http://www.dss.uniroma1.it/RePec/sas/wpaper/20114_johansen_2.pdf
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    References listed on IDEAS

    as
    1. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    2. 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.
    3. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    4. Juselius, Katarina, 2006. "The Cointegrated VAR Model: Methodology and Applications," OUP Catalogue, Oxford University Press, number 9780199285679.
    5. 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.
    6. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    7. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    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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