具有变点的AR-ARCH模型的估计  

Estimation of AR-ARCH Models with Change Points

作　　者：王敏[1,2] Wang Min(School of Mathematical Sciences,Xiamen University,Xiamen Fujian 361000,China;School of Mathematical Sciences,Guizhou Normal University,Guiyang 550001,China)

机构地区：[1]厦门大学数学科学学院,福建厦门361000 [2]贵州师范大学数学科学学院,贵阳550001

出　　处：《统计与决策》2020年第16期27-31,共5页Statistics & Decision

基　　金：国家自然科学基金资助项目(11861025);贵州师范大学资助博士科研项目(GZNUD[2017]27号);贵州省科学技术基金(黔科合J字LSK[2013]05号)。

摘　　要：文章提出了可以利用稀疏组Lasso方法对AR-ARCH模型中的变点进行估计。讨论了SGL方法的良好性质,并通过一个模拟分析,说明了在有变点的情况下,与前后向无窗估计方法相比得到更好结果的最小二乘方法对数据进行了更高阶的估计。有效的做法是先将数据的变点估计出来,通过一个Dirichlet过程对数据进行分类确定变点数,再利用SGL方法得到变点估计,这一做法是有效且精确的。This paper proposes that a sparse group Lasso method can be used to estimate the change points in AR-ARCH model. The paper first discusses the good properties of SGL method, and then makes a simulation analysis, showing a more encouraging result in the least squares method than the forward and backward windowless estimation method in the case of change points.The least squares method is also used to estimate the data of higher order. The effective way is as follows: The change point of data is estimated first, with a Dirichlet process used to classify the data and determine the variable points;and then the SGL method is used to get the change point estimation. This approach is both effective and accurate.

关 键 词：Lasso变点估计 惩罚最小二乘 自回归条件异方差 Dirichlet过程 

分 类 号：O21[理学—概率论与数理统计]