More discussions for granger causality and new causality measures

Abstract

Granger causality (GC) has been widely applied in economics and neuroscience to reveal causality influence of time series. In our previous paper (Hu et al., in IEEE Trans on Neural Netw, 22(6), pp. 829-844, 2011), we proposed new causalities in time and frequency domains and particularly focused on new causality in frequency domain by pointing out the shortcomings/limitations of GC or Granger-alike causality metrics and the advantages of new causality. In this paper we continue our previous discussions and focus on new causality and GC or Granger-alike causality metrics in time domain. Although one strong motivation was introduced in our previous paper (Hu et al., in IEEE Trans on Neural Netw, 22(6), pp. 829-844, 2011) we here present additional motivation for the proposed new causality metric and restate the previous motivation for completeness. We point out one property of conditional GC in time domain and the shortcomings/limitations of conditional GC which cannot reveal the real strength of the directional causality among three time series. We also show the shortcomings/limitations of directed causality (DC) or normalize DC for multivariate time series and demonstrate it cannot reveal real causality at all. By calculating GC and new causality values for an example we demonstrate the influence of one of the time series on the other is linearly increased as the coupling strength is linearly increased. This fact further supports reasonability of new causality metric. We point out that larger instantaneous correlation does not necessarily mean larger true causality (e.g., GC and new causality), or vice versa. Finally we conduct analysis of statistical test for significance and asymptotic distribution property of new causality metric by illustrative examples.

State Transitions During Discrimination Learning in the Gerbil Auditory Cortex Analyzed by Network Causality Metrics

“…When applying the core pairs for classification of CS+ and CS− stimuli, NC appears to be a more robust method with respect to extracting common features expressed at the inter-individual level. Hence, our study supports earlier reports which point out advantages of NC over GC in the analysis of neuronal data based on human EEG (Hu et al, 2011(Hu et al, , 2012(Hu et al, , 2015, and extends these findings to ECoG recordings in small rodents.…”

“…Granger Causality has been widely applied to identify the directional influence of system components in many different fields, including neuroscience (e.g., Ding et al, 2006;Wang et al, 2008;Bressler and Seth, 2011;Gao et al, 2011;Ge et al, 2012). In addition to GC, we use New Causality (NC) proposed by Hu et al (2011Hu et al ( , 2012. New Causality generalizes the concept of GC, such that it considers the proportion that X 1 occupies among all contributions to predict X 2 .…”

“…To address some of the limitations of Granger causality, Hu et al (2011) proposed the New Causality (NC) method, which considers the proportion that Y occupies among all contributions to predict X. As demonstrated by a number of applications, NC is often more robust than GC in revealing causal relationships in data (Hu et al, 2011(Hu et al, , 2012. NC and GC methods have been successfully applied in motor imagery to identify causal flows among regions Cz, C3, and C4, whereas NC shows significantly improved classification rate, as compared to GC (see, e.g., Hu et al, 2015;Kozma and Hu, 2015).…”

Pollution, economic growth, and COVID-19 deaths in India: a machine learning evidence

“…We used an algorithm in ML that could identify causal effects between the variables. Hu et al ( 2012 ) recommend a D2C algorithm on proportion-based causality using the Oryx 2.0.8 protocol in Apache. However, since an algorithm in ML needs many variables (remembering that the data are not interpreted as a time series), we completed mathematical transformations.…”

Neural Connectivity in Epilepsy as Measured by Granger Causality

“…By reviewing related literatures, it can be found that one of the most popular definitions for causality, which falls within modeling class of effective connectivity is GC. It was first introduced by Weiner in 1956 and later formalized by Granger in form of linear regression method in 1969 (Hu et al, 2012 ). GC can be simply defined as follows:…”