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What is the link between temperature and carbon dioxide levels? A Granger causality analysis based on ice core data


We use statistical methods to analyze whether there exists long-term causality between temperature and carbon dioxide concentration. The analysis is based on a the Vostok Ice Core data from 400,000 to 6,000 years ago, extended by the EPICA Dome C data which go back to 800,000 years ago. At first, to make the data equidistant, we reconstruct it by linear interpolation. Then, using an approximation of a piecewise exponential function, we adjust for a deterministic trend. Finally, we employ the Granger causality test. We are able to strongly reject the null hypothesis that carbon dioxide concentration does not Granger cause temperature as well as the reverse hypothesis that temperature does not Granger cause carbon dioxide concentration.

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  1. 1.

    The procedure to find modified break points is as follows: At first, we fix the last three break points (\(T_{5},T_{6}\) and \(T_{7}\)). We update the set \( T_{2},T_{3}\) and \(T_{4}\) by choosing the set that minimizes the residual sum of squares (RSS) within \(\pm 10\) time units of the break points of the previous set. Then, the updated \(T_{2},T_{3}\) and \(T_{4}\) are held fixed while the same procedure is applied to T 5, T 6 and T 7. The procedure is repeated until no further changes can be found.

  2. 2.

    In other words, the predictions of the last 50 observations are performed all at once, contrary to predicting one observation at a time and updating the parameter estimates before predicting the next one.

  3. 3.

    We also performed Portmanteau tests for higher lag lengths. We got nonrejections at the 5 % level for both series for lag lengths 1–5 and 8. These results are not given in the appendix but may be obtained from the authors at request.


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We are grateful to all the constructive comments and suggestions from the editor and the two anonymous referees, which greatly helped to improve the paper.

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Correspondence to Rolf Larsson.

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Kang, J., Larsson, R. What is the link between temperature and carbon dioxide levels? A Granger causality analysis based on ice core data. Theor Appl Climatol 116, 537–548 (2014).

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  • Break Point
  • Granger Causality
  • Carbon Dioxide Concentration
  • Granger Causality Test
  • Carbon Dioxide Level