带有分数布朗运动修正的GARCH模型

GARCH Model With Fractional Brownian Motion Correction

为了更加准确地刻画时间序列的长记忆性和厚尾性,文章建立了带有分数布朗运动增量平方项的GARCH模型,分析了模型的统计性质,给出了模型平稳解和各阶矩存在的条件,对模型的尾部性质和自相关函数的渐近性进行了讨论,证明了模型的长记忆性和厚尾性。最后通过数值模拟验证了理论结果的正确性。

In order to depict the long memory and fat tail of time series more accurately, this paper establishes a GARCH model with incremental square term of fractional Brownian motion, analyzes the statistical properties of the model, gives the conditions for the existence of stationary solutions and each moment of the model, and then discusses the tail properties of the model and the asymptotic behavior of autocorrelation function, proving the long memory and fat-tailed properties of the model. Finally,the paper verifies the correctness of the theoretical results by numerical simulation.