Dynamic patterns of daily lead-lag networks in stock markets

Abstract

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.

Key words:

• Stock market
• Lead-lag network
• Lead-lag effect
• Complex network
• Power-law distribution

JEL Classification:

• C59
• C81
• D85
• G19

Open Scholarship

This article has earned the Center for Open Science badges for Open Data and Open Materials through Open Practices Disclosure. The data and materials are openly accessible at https://github.com/liuchaos03/ssz-szse-stock-data and https://github.com/liuchaos03/Lead-lag-Networks-in-Stock-Markets.

Availability of data and material

Data available at https://github.com/liuchaos03/ssz-szse-stock-data, and Codes available at https://github.com/liuchaos03/Lead-lag-Networks-in-Stock-Markets.

Acknowledgements

We greatly thank the helpful discussions from Dr. Minheng Ni, Dr. Yiru Jiao, Dr. Ningyuan Fan and Ms. Xi Chen.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The result of the statistical tests for satisfying the power-law distribution in both markets is 0.093 and 0.576 (p value), respectively.

2 Given the null hypothesis that the variables follow an exponential distribution, the results of the statistical tests are 0.991 and 0.989 (p value), respectively, thus not rejecting the null hypothesis in both markets.

3 Since there are many standards for the division of stocks by industry, the standard chosen in this paper comes from the China Securities Regulatory Commission (CSRC).

Additional information

Funding

This work was supported by National Natural Science Foundation of China under [grant number 71771041] and Natural Science Foundation of Heilongjiang Province, China [grant number YQ2020G003].]