Time-varying pattern causality inference in global stock markets

Causality analysis can reveal the intrinsic interactions in financial markets. Though Granger causality test and transfer entropy method have successfully determined positive and negative causal interactions, they fail to reveal a more complex causal interaction, dark causality. Moreover, the causal relationship between variables may be time-varying. Thus, in this work, we are dedicated to determining the nature of causal interaction and explore the time-varying causality in global stock markets. To achieve this goal, pattern causality (PC) theory, cross-convergent mapping (CCM) theory, the sliding window method and complex networks are applied. By them, three causal interactions with different strength are revealed in global stock markets, and the causal strength is time-varying in different periods both in simulated systems and financial markets. While the dominant causal interaction is stable except for some stock pairs in frontier and emerging markets. In total, we determine the positive dominant causality in global stock markets; that is, the overall consistent trend among stocks can be explored. Additionally, we discover some exceptions that show negative dominant causality, where the reverse trend can be revealed among them; moreover, their dominant causality is time-varying. These uncertainties should receive great attention from investors and government managers.