Sampling distribution for single-regression Granger causality estimators

• 成果类型: Article
• 署名作者: Gutknecht, A. J.; Barnett, L.
• 署名单位: University of Gottingen; University of Sussex
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asad009
• 发表日期: 2023
• 页码: 933952
• 关键词: linear-dependence; factorization; feedback; tests

摘要

The 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 ?(2) distribution, which is well approximated by a & UGamma; 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 ?(2) and & UGamma;-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.