Sampling distribution for single-regression Granger causality estimators

A J Gutknecht and L Barnett

Biometrika, 2023, vol. 110, issue 4, 933-952

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.

Keywords: Generalized χ2 distribution; Granger causality; Likelihood-ratio test; Statistical inference (search for similar items in EconPapers)
Date: 2023
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