Wavelet Multiscale Granger Causality Analysis Based on State Space Models

Abstract

Granger causality (GC) is a popular method in causal linkage recovery and has been applied to various fields, such as economics and neuroscience. While the conventional Granger causality model is capable of identifying symmetrical causal relationships among variables, it is the asymmetric Granger causality that provides a more comprehensive perspective of the short- and long-term interactions between variables, which is of greater value for empirical study. Traditional vector autoregressive models lack the ability to explore multiscale information flow and are affected by the moving average component. Therefore, by combining the wavelet-based approach and state space model, we propose a new Granger causality analysis method to overcome the inherent limitation of vector autoregressive models and extend to multiscale causality exploration. Two simulations were conducted to compare the proposed approach to an existing wavelet-based method, and five evaluation indicators were utilized. The results indicate that the proposed method efficiently identifies the accurate asymmetric causalities at varying scales, while improving accuracy and reducing bias as compared to the current wavelet-based method. In conclusion, the combination of the wavelet approach and state space method enhances the multiscale causality detecting capability and can potentially contribute to multiscale Granger causality research.