Financial stocks in the industry chain interact notably because of close economic and technical relationships. Some participants pay particular attention to one industry chain and are concerned with different investment horizons. The motivation for this study is to offer more targeted information to various market participants who focus on different time scales in one industry chain from a systematic perspective by combining the GARCH-BEKK, heterogeneous network, and wavelet analysis methods. The findings are as follows: (1) For parties who prefer to take more risks to gain higher returns, scale 2 (4–8 days) is a good option, while long-term investment (32–128 days) is suitable for conservative investors. (2) In most cases, some links in the industry chain are particularly sensitive to changes in stocks in other links. (3) The influence, sensitivity, and intermediary of stocks in the industry chain on different time scales were explored, and participants could use the resulting information to monitor the market or select stocks. (4) The structures, key players, and industry chain attributes of the main transmission paths differ on multi-time scales. Risk transmission can be controlled by intercepting important spillover relations within the paths.

The relationship between investor attention and stock prices has been a topic of interest in economics. Previous studies have shown that the correlation relationship between the two changes with time. However, there are few studies to explore the time‐varying evolution of the relationship, as well as the transmission characteristics under important cycles. Thus, this paper is dedicated to discover the dynamic transmission characteristics of the correlation between investor attention and stock price. We selected the typical stocks of China’s energy industry, PetroChina and Sinopec, as the research objects, as they occupy a large market share and are representative. And the transaction data and attention data are used to build investor attention indicator. In order to reproduce the dynamic transmission process of correlation at different cycles, sliding time window and complex network are applied. The results show that PetroChina and Sinopec stocks have a weakly negative correlation between investor attention and stock price from 2017 to 2018. However, from the perspective of different cycles, the correlation has time‐varying characteristics. As the cycle grows, the types of transmission patterns of the five consecutive days of correlation between the two become less, but the transmission intensity between the modes increases and the transition becomes more regular and inclined. In addition, by mining the important transmission modes and main transmission paths under important periods, we find that the series modes of uncorrelated or weakly positive correlation for five consecutive days dominate the transition of modes in the networks. Also, the closed loop formed by these two important modes and related modes is the main transmission path. These findings can reveal the rules of the typical stock market in China’s energy industry and help investors with different investment cycle preferences make sound decisions.