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000873702 0247_ $$2arXiv$$aarXiv:1911.09625
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000873702 037__ $$aFZJ-2020-00925
000873702 1001_ $$0P:(DE-HGF)0$$aGutknecht, A. J.$$b0$$eCorresponding author
000873702 245__ $$aSampling distribution for single-regression Granger causality estimators
000873702 260__ $$c2019
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000873702 500__ $$aAaron Gutknecht was employed at the FZJ through the SMARTSTART Training program, project number DB001423.
000873702 520__ $$aWe show for the first time that, under the null hypothesis of vanishing Granger causality, the single-regression Granger-Geweke estimator converges to a generalised $\chi^2$ distribution, which may be well approximated by a $\Gamma$ distribution. We show that this holds too for Geweke's spectral causality averaged over a given frequency band, and derive explicit expressions for the generalised $\chi^2$ and $\Gamma$-approximation parameters in both cases. We present an asymptotically valid Neyman-Pearson test based on the single-regression estimators, and discuss in detail how it may be usefully employed in realistic scenarios where autoregressive model order is unknown or infinite. We outline how our analysis may be extended to the conditional case, point-frequency spectral Granger causality, state-space Granger causality, and the Granger causality $F$-test statistic. Finally, we discuss approaches to approximating the distribution of the single-regression estimator under the alternative hypothesis.
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000873702 588__ $$aDataset connected to arXivarXiv
000873702 7001_ $$0P:(DE-HGF)0$$aBarnett, L.$$b1
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000873702 9201_ $$0I:(DE-Juel1)INM-6-20090406$$kINM-6$$lComputational and Systems Neuroscience$$x0
000873702 9201_ $$0I:(DE-Juel1)IAS-6-20130828$$kIAS-6$$lTheoretical Neuroscience$$x1
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