Online Nonlinear Granger Causality Detection by Quantized Kernel Least Mean Square

Identifying causal relations among simultaneously acquired signals is an important challenging task in time series analysis. The original definition of Granger causality was based on linear models, its application to nonlinear systems may not be appropriate. We consider an extension of Granger causality to nonlinear bivariate time series with the universal approximation capacity in reproducing kernel Hilbert space (RKHS) while preserving the conceptual simplicity of the linear model. In particular, we propose a computationally simple online measure by means of quantized kernel least mean square (QKLMS) to capture instantaneous causal relationships.