Time-varying causality inference of different nickel markets based on the convergent cross mapping method

Most previous studies ignored the nonlinear dynamic mechanism of the interaction between variables when exploring the causal relationship between economic and financial time series. Moreover, the dynamic interactions between these prices are time-varying. Therefore, we divide the whole time series into segments and use the convergent cross mapping method in each window to detect the causality among prices, which are defined as the causality patterns. The transition of these patterns over time can form a causal evolutionary network. Thus, we analyze and explore the time-varying characteristics of causality among spot prices, futures prices and stock prices in nickel markets through the structural characteristics of the constructed network. The results indicate that the diversity of causality patterns decreases with an increasing time scale. We selected 600 days as the study time scale to ensure the diversity and stability of causality patterns. However, only a few patterns play an important role in the evolution of causality, and when identified from different perspectives, the important patterns are not the same. However, these important patterns are all characterized by the fact that the influence of the stock market on other nickel markets is weaker than the influence of other nickel markets on the stock market. Moreover, some causality patterns can form clusters due to their frequent interactions. There is a certain preference in the transition between patterns or clusters. Our results can help market participants understand and monitor the dynamic process of causality among nickel prices in different markets.