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Geometric and Long Run Aspects of Granger Causality

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  • Majid M. Al-Sadoon

Abstract

This paper extends multivariate Granger causality to take into account the subspaces along which Granger causality occurs as well as long run Granger causality. The properties of these new notions of Granger causality, along with the requisite restrictions, are derived and extensively studied for a wide variety of time series processes including linear invertible process and VARMA. Using the proposed extensions, the paper demonstrates that: (i) mean reversion in L2 is an instance of long run Granger non-causality, (ii) cointegration is a special case of long run Granger non-causality along a subspace, (iii) controllability is a special case of Granger causality, and finally (iv) linear rational expectations entail (possibly testable) Granger causality restriction along subspaces.

Suggested Citation

  • Majid M. Al-Sadoon, 2013. "Geometric and Long Run Aspects of Granger Causality," Working Papers 682, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:682
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    1. Some Weekend Reading
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2013-11-01 22:41:00
    2. Some Weekend Reading
      by ? in R-bloggers on 2013-11-01 22:41:00

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    Cited by:

    1. Al-Sadoon, Majid M., 2018. "The Linear Systems Approach To Linear Rational Expectations Models," Econometric Theory, Cambridge University Press, vol. 34(3), pages 628-658, June.
    2. Al-Sadoon, Majid M., 2019. "Testing subspace Granger causality," Econometrics and Statistics, Elsevier, vol. 9(C), pages 42-61.
    3. Ikegami, Masako & Wang, Zijian, 2016. "The long-run causal relationship between electricity consumption and real GDP: Evidence from Japan and Germany," Journal of Policy Modeling, Elsevier, vol. 38(5), pages 767-784.
    4. Majid M. Al-Sadoon, 2014. "A general theory of rank testing," Economics Working Papers 1411, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 2015.
    5. Triacca, Umberto, 2018. "Granger causality between vectors of time series: A puzzling property," Statistics & Probability Letters, Elsevier, vol. 142(C), pages 39-43.

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    More about this item

    Keywords

    Granger causality; long run Granger causality; L2-mean-reversion; rho-mixing; cointegration; VARMA; controllability; Kalman Decomposition; linear rational expectations;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • 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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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