提出混合隐马尔可夫模型,更好模拟股市收益的厚尾与波动聚集特征。
Hybrid Hidden Markov Model for Modeling Equity Excess Growth Rate Dynamics: A Discrete-State Approach with Jump-Diffusion
- 将收益分段为拉普拉斯分位数状态,引入泊松跳跃持续机制
- 在十年日度数据上实现高通过率分布拟合与部分波动聚集再现
- 适合多资产生成,优于传统因子模型,尤其在相关性还原上
生成保留真实市场统计特性的合成金融时间序列对压力测试、风险模型验证和情景设计至关重要。现有方法难以同时复现重尾分布、近零线性自相关和持续波动聚集。本文提出一种混合隐马尔可夫框架,将超额收益率离散化为拉普拉斯分位数定义的状态,并通过泊松跳跃持续机制增强状态切换,以实现合理的尾部状态停留时间。参数通过直接转移计数估计,避免使用 Baum-Welch EM 算法,可扩展至424个资产的流水线。在十年日度股权数据上的应用显示,该框架在样本内和样本外均实现了高分布通过率,部分再现了标准切换模型所缺失的波动聚集。单一模型无法兼顾所有特性:GARCH(1,1) 更好复现波动聚集但分布检验失败;标准HMM无跳跃则通过更多分布检验但无法生成波动聚集。本框架整体表现最平衡。对于多资产生成,基于拷贝的依赖模型在保持各资产边际HMM分布的基础上,显著优于单指数因子基线,在资产分布准确性和相关性还原方面均表现更优。
原文摘要 · Abstract (English)
Generating synthetic financial time series that preserve the statistical properties of real market data is essential for stress testing, risk model validation, and scenario design. Existing approaches struggle to simultaneously reproduce heavy-tailed distributions, negligible linear autocorrelation, and persistent volatility clustering. We developed a hybrid hidden Markov framework that discretized excess growth rates into Laplace quantile-defined states and augmented regime switching with a Poisson jump-duration mechanism to enforce realistic tail-state dwell times. Parameters were estimated by direct transition counting, bypassing the Baum-Welch EM algorithm and scaling to a 424-asset pipeline. Applied to ten years of daily equity data, the framework achieved high distributional pass rates both in-sample and out-of-sample while partially reproducing the volatility clustering that standard regime-switching models miss. No single model was best at everything: GARCH(1,1) better reproduced volatility clustering but failed distributional tests, while the standard HMM without jumps passed more distributional tests but could not generate volatility clustering. The proposed framework delivered the most balanced performance overall. For multi-asset generation, copula-based dependence models that preserved each asset's marginal HMM distribution substantially outperformed a Single-Index Model factor baseline on both per-asset distributional accuracy and correlation reproduction.
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