Descriptive statistics of the main variables.

Synchronization, which has been a common natural phenomenon, occurs frequently in complex financial systems and is an important contagion mechanism for systemic financial risks and even financial crises. In view of this, we construct a coupled stochastic volatility model and its volatility synchronization analysis framework and combine machine learning methods and rolling cycle window to propose a prediction method for dynamic volatility synchronization. Taking the Shanghai Composite Index (SSEC) and Shenzhen Component Index (SZI) as binary synchronization examples, we analyze the dynamic forecasting performance of the proposed method in an in-sample and out-of-sample empirical comparison by combining multiple loss functions and Superior Predictive Ability (SPA) tests for high-frequency data. It is found that the in-sample estimates of our proposed model are highly consistent with the market behavior and that the model outperforms other models in predicting stock market volatility synchronization accuracy. In addition, by combining dynamic simulation with multivariate empirical mechanism analysis, our methodology not only explores synchronization dynamics but also identifies significant risk events, providing a comprehensive framework for understanding complex system behaviors.