Granger Causality's Shortcomings and New Causality Measure
Sanqing Hu, Yu Cao, Jianhai Zhang, Wanzeng Kong, Kun Yang, Yanbin Zhang, Xun Li · 2009
Abstract. Granger causality (GC) is one of the most popular measures to re-veal causality influence of time series and has been widely applied in economics and neuroscience due to its simplicity and easy implementation. In this paper, we show that GC in time domain cannot correctly determine how strongly one time series influences the other when there is directional causality between two time series, that is, a larger GC value does not necessarily mean higher real causality, or vice versa. On the other hand, we propose one novel causality measure in time domain for the linear regression model, called new causality, which is more rea-sonable and understandable than the traditional GC. Especially, from one simple example we point out that in time domain both of new causality and GC adopt the concept of proportion, but they are defined on two different equations where one equation (for GC) is only part of the other equation (for new causality), thus, new causality is a natural extension of GC and has a sound conceptual/theoretical basis, and GC is not the desired causal influence at all. By several examples we confirm that new causality measure has distinct advantages over GC. The pro-posed new causality measure may have wide potential applications in economics and neuroscience.