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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.

Previous studies detected the spillover relations among stocks and identified the spillover roles of stocks. However, due to the participants with different dealing frequencies, the spillover effects in the stock market present multiscale features, then which time-frequency domain dominates the spillover in the stock market? Take Chinese energy stocks as an example, this paper examines the return spillover effects of the energy stock market under each time-frequency domain. We find significant return spillover in the Chinese energy stock market under different time scales, and the spillover effect under the time scale of 32–64 days contributes the most to the spillover in the whole energy stock market. Then we take further research on the directional spillovers, spillovers between energy stocks and spillovers between energy industries to detect who plays leading positions under each time scale. We divide the stocks into four roles, and find that it is different role that plays a leading position under each time scale. Furthermore, a small number of spillover relationships between energy stocks carry a large part of the total spillover quantities, and coal and consumable fuel-related stocks play an important role in the spillover of Chinese energy stocks. The robustness of our results is proved by additional tests with different forecast horizons. Our paper contributes to the literature by examining the multiscale spillover effect in the Chinese energy stock market, which provides references for market participants on investment horizons choosing, stocks selection and risk aversion.

This study investigates the influential energy stocks in the China stock market between 2005.1.4 and 2018.4.3. The influential energy stock is defined as a stock whose fluctuations could lead to the rises and falls of many other stocks in the energy sector, which have attracted much attention from investors and policymakers. To achieve this objective, the BEKK-GARCH model is used to capture the volatility spillover among energy stocks, the more spillover correlations a stock has the more influential it is. Furthermore, complex network theory is introduced to give more specific and precise quantifications of the stock influence. Validity testing of the methods shows that the PageRank algorithm is the most suitable method for identifying influential energy stocks. The results reveal the time-varying features of influential energy stocks, which indicate the weak momentum effect and strong reversal effect of the China stock market. Furthermore, most of the top-10 influential energy stocks are belong to the industry of power and utilities, and the investors are suggested to make reverse trading strategies around the influential electricity stocks. Moreover, petroleum exploitation and petroleum processing are the most two influential subindustries, and the policymakers are suggested to pay much attention to prevent the aggregate risks of the oil stocks which belong to these two subindustries.