协变量驱动的随机系数自回归模型参数估计

发布时间：2018-01-08 10:36

本文关键词：协变量驱动的随机系数自回归模型参数估计　出处：《吉林大学》2017年硕士论文　论文类型：学位论文

【摘要】：时间序列分析一直是统计学的一个重要分支,主要分为线性时间序列模型与非线性时间序列模型.关于线性时间序列模型的研究结果目前已经比较成熟,但由于实际生活中的部分数据不符合线性时间序列模型.因此,在近几十年来,非线性时间序列模型越来越受到国内外学者的关注,并取得了不错的研究成果.其中,随机系数自回归模型是非线性时间序列的一种,它与Logistic回归模型在实际生活中都有着广泛的应用,但目前国内外学者将两者结合起来的研究还非常稀少.基于此,本文提出了一个全新的随机系数自回归模型:其中随机误差序列{(?)t}i.i.d服从Laplace(0,1)分布,自回归系数αt是随机变量,服从包含协变量Z的Logistic回归模型,这也是本文的创新之处.本文的主要工作是运用基于条件期望的最小二乘估计、极大似然估计及贝叶斯估计方法对一阶Logistic回归模型的参数β1,β2进行估计.但是,Logistic回归模型中涉及到了对数函数,函数表达式较为复杂,因此在做参数估计时考虑使用Taylor展开近似,将复杂的表达式化为多项式的形式,得出近似估计表达式.而对不能解出显式参数估计表达式的方程运用Matlab利用数值分析方法给出数值解.最后对所提出的方法进行数值模拟和实证分析,比较不同方法的优劣并给出结论.
[Abstract]:Time series analysis has been an important branch of statistics, mainly divided into linear time series model and nonlinear time series model. However, some of the data in real life do not accord with the linear time series model. Therefore, in recent decades, the nonlinear time series model has attracted more and more attention from domestic and foreign scholars. The random coefficient autoregressive model is a kind of nonlinear time series, which is widely used in real life with Logistic regression model. However, there are few researches on the combination of the two at home and abroad. Based on this, a new autoregressive model with random coefficients is proposed in this paper: where the random error sequence {? The autoregressive coefficient 伪 t was a random variable, and the Logistic regression model containing covariable Z was used. This is also the innovation of this paper. The main work of this paper is to use the least square estimation based on conditional expectation, maximum likelihood estimation and Bayesian estimation to the parameter 尾 1 of the first-order Logistic regression model. But the logarithmic function is involved in the logistic regression model, and the expression of the function is more complicated. Therefore, the Taylor expansion approximation is considered in the parameter estimation. Transform complex expressions into polynomial forms. The approximate estimation expression is obtained. Matlab is used to give the numerical solution for the equation which can not solve the explicit parameter estimation expression. Finally, the numerical simulation and empirical analysis of the proposed method are carried out. . The advantages and disadvantages of different methods are compared and the conclusions are given.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1

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