AI 中文总结
该研究结合多时间尺度异构数据，提出含经典聚类模型的霍克斯过程降雨建模方法，发现粗尺度降雨收敛到赫斯特指数近0的粗糙分数过程，建立降雨动力学与金融模型的联系。
AI 中文摘要
我们提出了一种新方法，用于结合不同时间尺度的异构数据源对降雨进行建模。降雨单元的连续到达被纳入霍克斯（Hawkes）过程形式体系，该体系包含经典的巴特利特-刘易斯（Bartlett-Lewis）模型和内曼-斯科特（Neyman-Scott）模型，从而提供了更灵活的聚类表示。对高频降雨数据（数年的分钟尺度数据）的分析表明，具有重尾幂律核的临界霍克斯过程，相较于经典模型和其他核规范，拟合效果更优。受贾森和罗森鲍姆（Jaisson and Rosenbaum，2016）启发的标度论证表明，粗时间尺度下的聚合降雨会收敛到赫斯特指数接近零的粗糙分数过程。这一预测得到了低频数据的实证支持（涵盖数百年至数千年的年度观测数据），其中基于气象站的直接观测或树轮记录等代用重建数据，估算出的赫斯特指数介于0.01至0.1之间。这些结果建立了降雨动力学与定量金融中用于市场微观结构和波动率的模型之间的联系，也为赫斯特和曼德尔布罗特最初研究的经典标度现象提供了新视角。
英文摘要
We propose a new approach to model rainfall by combining heterogeneous data sources at different time scales. Continuous arrivals of rain cells are incorporated into a Hawkes process formalism that encompasses the classical Bartlett-Lewis and Neyman-Scott models, thereby providing a more flexible representation of clustering. Analysis of high frequency rainfall data (at the minute scale over several years) indicates that critical Hawkes processes with heavy-tailed power-law kernels yield a superior fit relative to classical models and alternative kernel specifications. Scaling arguments inspired by Jaisson and Rosenbaum (2016) imply that aggregated rainfall at coarse time scales converges to a rough fractional process with Hurst exponent close to zero. This prediction is supported by empirical evidence from low-frequency data (annual observations spanning centuries to millennia), where the Hurst exponent is estimated to lie between 0.01 and 0.1 based on either direct observations from weather stations or proxy reconstructions such as tree-ring records. These results establish a connection between rainfall dynamics and models developed in quantitative finance for market microstructure and volatility. They also provide a new perspective on classical scaling phenomena originally studied by Hurst and Mandelbrot.
