由分数Brown运动驱动的EGARCH模型  

EGARCH Model Driven by Fractional Brownian Motion

作　　者：王玮莹 韩月才[1] WANG Weiying;HAN Yuecai(College of Mathematics,Jilin University,Changchun 130012,China)

机构地区：[1]吉林大学数学学院,长春130012

出　　处：《吉林大学学报(理学版)》2025年第1期41-46,共6页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12471417).

摘　　要：针对传统EGARCH模型难以捕捉长记忆性的问题,通过引入分数Brown运动提出一个fBm-EGARCH模型,给出模型的二阶矩、四阶矩及协方差函数性质,并理论证明其长期记忆性.数值模拟结果表明,该模型不仅能准确捕捉短期波动,还能反映长期记忆性,从而验证了模型的有效性.Aiming at the problem that the traditional EGARCH model was difficult to capture long-term memory,we proposed an fBm-EGARCH model by introducing fractional Brownian motion.We gave the second-order moment,the fourth-order moment and covariance function properties of the model,and theoretically proved its long-term memory.Numerical simulation results show that the model can not only accurately capture short-term fluctuations,but also reflect long-term memory,which verifies the effectiveness of the model.

关 键 词：EGARCH模型 分数Brown运动 长期记忆性 流动性 

分 类 号：O211.61[理学—概率论与数理统计]