A general statistical framework for assessing Granger causality

Abstract

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.