发表机构
Department of Mathematics and Statistics, School of Technology and Innovations, University of Vaasa（瓦萨大学技术与创新学院数学与统计系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种结合Metropolis-Hastings采样的EM算法，用于混合分数Merton跳跃扩散模型的参数估计，该模型结合分数布朗运动与复合泊松跳跃过程，捕捉金融时间序列的长记忆性和跳跃行为，并在OMXH25指数上验证了其可靠性和计算效率。
AI 中文摘要
本文提出了一种结合Metropolis-Hastings采样的期望最大化（EM）算法，用于混合分数Merton跳跃扩散模型中的参数估计。该模型结合分数布朗运动以捕捉长程依赖性，以及复合泊松跳跃过程以描述金融收益中的突变。在E步中，通过马尔可夫链蒙特卡洛采样推断潜在跳跃过程，而M步则通过最大化期望完整数据似然来更新模型参数。在适当的正则条件下，建立了所提出估计量的一致性和渐近正态性。该方法应用于赫尔辛基股票指数（OMXH25）。所提出的估计框架为建模同时表现出长记忆依赖性和跳跃行为的金融时间序列提供了一种可靠且计算高效的方法。
英文摘要
This paper proposes an Expectation--Maximization algorithm with Metropolis--Hastings sampling for parameter estimation in a Mixed Fractional Merton Jump Diffusion model. The model combines fractional Brownian motion to capture long-range dependence with a compound Poisson jump process to describe abrupt movements in financial returns. The latent jump process is inferred during the E-step using Markov Chain Monte Carlo sampling, while the M-step updates the model parameters by maximizing the expected complete-data likelihood. The consistency and asymptotic normality of the proposed estimator are established under suitable regularity conditions. The methodology is applied to the Helsinki Stock Index (OMXH25). The proposed estimation framework provides a reliable and computationally efficient approach for modeling financial time series exhibiting both long-memory dependence and jump behavior.
Comments22 pages, six figures
