The Coupling Spectrum: a New Method for Detecting Temporal Nonlinear Causality in Financial Time Series

Identifying dynamic causal relationships between financial time series may help explain market dynamics. The Granger causality (G-causality) test is a method to detect linear causal relationships between time series. However, there exists significant evidence for nonlinear causality between financial time series. Hence, several nonlinear extensions of G-causality (NLG-causality) were proposed. Moreover, a new method called the coupling spectrum (CS) was recently proposed to find the nonlinear causal relationship between two time series. In many financial cases, the direction of causality is changing over time. In this work, we adapt the NLG-causality and CS methods by using a moving window technique to identify possible causality changes over time. We compare the performance of the adapted CS and NLG-causality methods on a simulated temporal nonlinear causal system and a real data set the stock prices of Apple Inc. and Microsoft Corporation. The simulated and empirical results show that the CS method is more robust than the NLG-causality method and that CS is capable of dealing with time-varying nonlinear causality between financial time series.