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@ARTICLE{Gutknecht:873702,
      author       = {Gutknecht, A. J. and Barnett, L.},
      title        = {{S}ampling distribution for single-regression {G}ranger
                      causality estimators},
      reportid     = {FZJ-2020-00925},
      year         = {2019},
      note         = {Aaron Gutknecht was employed at the FZJ through the
                      SMARTSTART Training program, project number DB001423.},
      abstract     = {We 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.},
      cin          = {INM-6 / IAS-6 / INM-10},
      cid          = {I:(DE-Juel1)INM-6-20090406 / I:(DE-Juel1)IAS-6-20130828 /
                      I:(DE-Juel1)INM-10-20170113},
      pnm          = {574 - Theory, modelling and simulation (POF3-574) /
                      Smartstart - SMARTSTART Training Program in Computational
                      Neuroscience (90251)},
      pid          = {G:(DE-HGF)POF3-574 / G:(EU-Grant)90251},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {1911.09625},
      howpublished = {arXiv:1911.09625},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:1911.09625;\%\%$},
      url          = {https://juser.fz-juelich.de/record/873702},
}