Dynamic patterns of daily lead-lag networks in stock markets

The lead-lag relationship between stocks is an interesting phenomenon, which has been empirically seen to widely exist in stock markets. This paper aims to discover the dynamic patterns of the daily lead-lag relationships between stock pairs, to detect the features of the discovered dynamic patterns, and to explore which factors significantly affect the emergence of the feature. To this end, a series of statistical analyses is conducted to find that the (longest) successive lead-lag days satisfy a power-law distribution in the two mainland stock markets in China, which answers the question regarding the dynamic pattern. Note that the heavy tail of the power-law distribution is the core of the discovered dynamic pattern. A formal and solid definition of the lead-lag effect is provided by statistical testing, and then the corresponding detection method is designed and applied to obtain the heavy tail. Finally, an empirical study of the detected stocks with lead-lag effect is further conducted via an exponential random graph model (ERGM). Our work adds new knowledge to the lead-lag phenomenon in the financial domain, provides a formal definition of the lead-lag effect and proposes a new detection method benefiting future studies on the lead-lag relationship in financial markets. It further contributes to the existing relevant literature by a deep understanding of which factors cause the emergence of the power-law distribution discovered.