To investigate the price fluctuation mechanism of stock markets, this research aims to develop a novel stochastic financial model based on Potts dynamics and compound Poisson process. The new model considers two aspects: information interaction among traders and the uncertain events outside the system. Then, three different volatility statistics (return series \(r_t\), absolute return series \(|r_t|\) and volatility duration average intensity \(V_t\)) are introduced to explore the volatility and complexity properties of the proposed model. The descriptive statistical methods, such as basic statistical properties and distribution analysis, are studied to validate the practicable of the proposed stochastic financial model. The permutation Lempel-Ziv complexity of moving average series is referred to different volatility sequences to evaluate the complexity of the simulative data from proposed model and the real data from stock market. Moreover, the complexity analysis of fractional sample entropy and multiscale fractional sample entropy is improved to illustrate the complexity of volatility behaviors in different scales. Compared with the real stock data, the empirical results demonstrate that the new model could reproduce the fluctuation and volatility behaviors of real stock markets to some extent.

为了研究股票市场的价格波动机制，本研究旨在开发一种基于 Potts 动力学和复合泊松过程的新型随机金融模型。新模型考虑了两个方面：交易者之间的信息交互和系统外的不确定事件。然后，三种不同的波动率统计数据（回报序列\(r_t\)，绝对回报序列\(|r_t|\)和波动率持续时间平均强度\(V_t\)) 被引入来探索所提出模型的波动性和复杂性特性。研究了描述性统计方法，如基本统计特性和分布分析，以验证所提出的随机财务模型的实用性。移动平均序列的置换 Lempel-Ziv 复杂度参考不同的波动率序列来评估所提出模型的模拟数据和股票市场的真实数据的复杂度。此外，改进了分数样本熵和多尺度分数样本熵的复杂性分析，以说明不同尺度波动行为的复杂性。与真实库存数据相比，