Akaike Causality - Noise Contribution Ratio and Generalized Partial Directed Coherence

This function plots the Noise Contribution Ratio and the Generalized Partial Directed Coherence.

Akaike's Noise Contribution Ratio is a tool to show the strength of causal relationship among multiple variables based on partitioning the power spectral density of an optimal autoregressive model, whereas the Generalized Partial Directed Coherence is a tool to identify presence and absence of direct causality between 2 variables given the other variables. Akaike's Noise Contribution Ratio focus on decomposing spectral power to variables, therefore the row sum is 1, whereas Generalized Partial Directed Coherence focus on decomposing spectral power from variables, therefore the column sum is 1. Note that NCR and GPDC are the same in the bivariate case. Users should not use GPDC values to interpret causality strength in the case of 3 or more variables.
References:
[1] Akaike H and Nakagawa T (1988) Statistical Analysis and Control of Dynamic Systems (Mathematics and its Applications) ISBN-10: 9027727864
[2] Wong KFK and Ozaki T (2007) "Akaike Causality in State-Space", Biological Cybernetics 97: 151-157. DOI: 10.1007/s00422-007-0165-1
[3] De Brito CS, Baccala LA, Takahashi DY and Sameshima K (2010) "Asymptotic Behavior of Generalized Partial Directed Coherence" 32nd EMBC 1718-1721. DOI: 10.1109/IEMBS.2010.5626856