A general statistical framework for assessing Granger causality

Assessing the causal relationship among multivariate time series is a crucial problem in many fields. Granger causality has been widely used to identify the causal interactions between continuous-valued time series based on multivariate autoregressive models in the Gaussian case. In order to extend the application of the Granger causality concept to non-Gaussian time series, we propose a general statistical framework for assessing the causal interactions. In this study, the Granger causality from a time series x₂ to a time series x₁ is assessed based on the relative reduction of the likelihood of x₁ by the exclusion of x₂ compared to the likelihood obtained using all the time series. Simulation results indicated that the proposed algorithm accurately predicted nature of interactions between discrete-valued time series as well as between continuous-valued time series.