双线性模型的尾部概率性质及收敛性质  

Probability Behavior and Convergence Behavior of a Simple Bilinear Model with Tail Weights

作　　者：刘维奇[1] 孟银凤[1] 

机构地区：[1]山西大学数学科学学院,太原030006

出　　处：《应用数学学报》2007年第3期422-436,共15页Acta Mathematicae Applicatae Sinica

基　　金：山西省自然科学基金(20031005)资助项目.

摘　　要：实践中,许多来自电信、金融和经济领域的数据呈现出非线性、重尾特征．双线性模型就是刻划这类数据的一种类型．基于此,本文研究了由重尾噪声变量列{Z_t}生成的一类简单的平稳的双线性模型X_t=cX_t-_kZ_(t-l)+Z_t,t=0,±1,±2,…．首先我们验证了在一定条件下模型是稳定的,并在此基础上研究了模型的尾部概率性质及其弱极限性质．在研究弱极限性质时,由于方差不存在,我们并未采用通常的研究方法,而是运用点过程理论对其进行了分析和研究．Currently an important topic in time series analysis is how to deal with data which exhibit features like long range dependence, nonlinearity and heavy tails. Many datasets from fields such as telecommunications , finance and economics appear to be compatible with the assumption of heavy tailed marginals. The class of bilinear models is often used to describe this kind of data. In this paper, We consider a simple stationary bilinear model Xt = cXt-kZt-1 ＋ Zt, t = 0, ＋1, ±2,… generated by heavy tailed noise variables {Zt}. Firstly we give a detailed analysis of the stationarity of the model if it satisfies certain condition. Based on it, We mainly study probability behavior on tail weights under the circumstance of heavy tailed noise variables, and a analysis of weak limit behavior is given by means of point process methods because {Xt} has infinite variance.

关 键 词：重尾分布 点过程 稳定解 均值测度 

分 类 号：O211.6[理学—概率论与数理统计]