Can topological transitions in cryptocurrency systems serve as early warning signals for extreme fluctuations in traditional markets?

This study employs persistent homology in Topological data analysis (TDA) to investigate the early warning potential of the cryptocurrency system for fluctuations in traditional financial markets. By examining the time-varying characteristics of the system's topological structure, we aim to find evidence that these transitions can predict extreme market fluctuations. Our research indicates that cryptocurrencies exhibit stylized facts similar to those of traditional financial assets and that the overall topological structure of the cryptocurrency system demonstrates significant temporal evolutionary characteristics. Moreover, empirical findings reveal a notable time lag between the turning points in the topological structure of the cryptocurrency system and extreme fluctuations in the U.S. stock market. Specifically, these turning points typically occur 0-5 calendar days before the market fluctuations, suggesting their potential as early warning signals. The sensitivity of both in-sample and out-of-sample warning results reaches 60%, supporting the practical applicability of this approach. Extreme fluctuations not predicted are primarily caused by sudden external events, indicating that the proposed method is better suited for early warning of endogenous market volatility. We also explain these results from the perspectives of market efficiency theory, information spillover effects, and behavioral finance. Ultimately, this analysis enhances our understanding of the cryptocurrency market's evolutionary process and provides valuable insights for both investors and regulators.