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Sampling distribution for single-regression Granger causality estimators

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  • A J Gutknecht
  • L Barnett

Abstract

SummaryThe single-regression Granger–Geweke causality estimator has previously been shown to solve known problems associated with the more conventional likelihood ratio estimator; however, its sampling distribution has remained unknown. We show that, under the null hypothesis of vanishing Granger causality, the single-regression estimator converges to a generalized χ2 distribution, which is well approximated by a Γ distribution. We show that this holds too for Geweke’s spectral causality averaged over a given frequency band, and derive explicit expressions for the generalized χ2 and Γ-approximation parameters in both cases. We present a Neyman–Pearson test based on the single-regression estimators, and discuss how it may be deployed in empirical scenarios. We outline how our analysis may be extended to the conditional case, point-frequency spectral Granger causality and the important case of state-space Granger causality.

Suggested Citation

  • A J Gutknecht & L Barnett, 2023. "Sampling distribution for single-regression Granger causality estimators," Biometrika, Biometrika Trust, vol. 110(4), pages 933-952.
    • Handle: RePEc:oup:biomet:v:110:y:2023:i:4:p:933-952.
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    References listed on IDEAS

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    1. André Klein & Guy Melard & Toufik Zahaf, 2000. "Construction of the exact Fisher information matrix of Gaussian time series models by means of matrix differential rules," ULB Institutional Repository 2013/13742, ULB -- Universite Libre de Bruxelles.
    2. Dufour, Jean-Marie & Taamouti, Abderrahim, 2010. "Short and long run causality measures: Theory and inference," Journal of Econometrics, Elsevier, vol. 154(1), pages 42-58, January.
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