多元AR（p）模型的估计理论-应用数学专业毕业论文.docx

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摘 要
本文系统地研究了多元弱平稳序列自回归模型AR(p)的参数估计方法及性状。首先,借助Hi]bert空间理论,提出了距离估计的d~解,给出了d一解的必要条件,这个条件在线性函数类里即是极小二乘估计法,d一解的必要条件满足的方程实质上将极小二乘估计法推广到多函数及非线性函数类。再两,详细地研究了多元弱平稳序列自回归模型AR(p)的参数经典的矩的替代估计和极大似然估计,获得矩的替代估计的一致性的结果。对基于Gauss白噪声假设多元弱平稳序列自回归模型的均值、白噪声的协方差阵的极大似然估计都有依分布收敛到多元正态分布的统计性质。作者用高阶微分方程化一阶微分方程组的方法,获{:寻多元弱平稳序列P阶自回归模型的一步滑动平均表达式,证明了AR(p)的是一个更高维的幂级数的线性过程,从而,说明了AR(p)关于序列依概率成立的充要条件是: 该模型更高维的幂级数的线性过程的表达式中系数矩阵D的谱范数A<1。AR(p、简化后给理论分析AR(p)的参数带来极大的方便:可以得到Z的二阶协方差阵参数r@)的正交性特征,,这一特征用来检验卫是否为多维向量P阶自回归过程;又可以得到 AR(p)的整体预报式,整体的预报式克服了传统的线性预报理论多阶不确定性。
关键宇:弱平稳,自回归,,估计,预报。
ABSTRACT
This dissertation deals with how to estmaate parameters of a model of multivariable weak stable Auto—regression Equation on time series(marked by agfp))and formulizes properties of up with a new notion,d-solution, which is applied to the distance estimation,by vktue of Hilbert space;furthermore, the dissertation has gained a necessary condition which is identity of minimum mean,square value in linear function classes,so that d-solution extends minimum mean·square value within the domain of nonlinear function equation or equation system;and,the dissertation studies in detail the classical moment estimation and maximal likelihood estimation on the parameters of AR(p),a series of theorems in the estimation section mows the moment estimators are consistent on the ground of large samples,likewise,those distribution functions of the estimated parameters
accord to maximum likelihood estimation converge Gauss distribution if the white
noise is important result is the one—order expression of aR(p)
×一Dr,一1+Ef from paralleling a high-order differential equation transformation into a one—order differential equation system,the one-order expression exposes that the Ag(p)is only a certain more-multivariable power series process
¨t∑二D‘E一·
And,if a process is described