Sampling distribution for single-regression Granger causality estimators

Gutknecht, A. J.; Barnett, L.

Preprint

FZJ-2020-00925

Sampling distribution for single-regression Granger causality estimators

Gutknecht, A. J. (Corresponding author)FZJ* ; Barnett, L.

2019

This record in other databases:

Please use a persistent id in citations: http://hdl.handle.net/2128/24272

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.

Note: Aaron Gutknecht was employed at the FZJ through the SMARTSTART Training program, project number DB001423.

Contributing Institute(s):

Research Program(s):

Appears in the scientific report 2019

Database coverage:
OpenAccess