Multi-scale pattern causality of the price fluctuation in energy stock market

Pattern causality, as a nonlinear causality test method, can reveal the positive, negative and dark causal relations between time series and evaluate the causal strength quantitatively. In this study, we provide a comprehensive understanding about the nonlinear pattern causality of energy stock market from a multiscale perspective. By synthetically adopting the maximal overlap discrete wavelet transformation (MODWT) method, pattern causality (PC) theory and network analysis method, a systemic framework is constructed, and some interesting results are obtained. (1) Three types of causal strength exhibit inverted U-shape with the increase of time scales, and dark causality accounts for a relatively high percentage. (2) The dark causal strength is strongest in D5 (32–64 days) and D6 (64–128 days), meaning that the uncertainty of the causal relationships in energy stock market obviously increases in the long term. (3) The coal-related stocks have high influence, sensitivity and intermediary, which deserve more attention from investors. This work can provide valuable suggestions for regulators and investors with different risk preferences.