近平稳二阶自回归过程中参数估计量的渐近分布及中偏差原理

发布时间：2018-05-06 19:45

本文选题：渐近分布 + Durbin-Watson统计量　；参考：《南京航空航天大学》2015年硕士论文

【摘要】：概率论是研究随机现象统计规律性的数学分支,它在自然科学、社会科学和生产实际中都有着广泛的应用.大偏差原理理论自上世纪六十年代引入,其研究的是一种遍历性收敛速度的问题,经许多学者的开拓发展,现已经称为概率论的一个重要分支.它在偏微分,马氏过程,动力系统随机扰动,统计,保险与金融等众多领域有着广泛的应用.在金融经济中,股票价格的变化过程大致呈现出自回归模型的形式,通过对参数估计量的分析可以研究数据序列所遵从的统计规律,从而对股票价格进行有效的控制和预测.本文由四章构成：第一章,简单回顾大偏差原理理论的基本概念以及要用到的结论,介绍本文的研究对象与已知结论,然后在此基础上给出本文的研究动机.第二章,对于文中所研究的模型加以介绍,给出我们所得到的结果.第三章,我们分别给出了估计量θn,ρn以及Durbin-Watson统计量Dn渐近分布的证明.首先将θn-θn*分解成分式的形式,利用鞅的中心极限定理得到分子的渐近分布,以及分母弱收敛到其期望,从而由Slutsky's引理得到估计量θn的渐近分布.其次,利用二维鞅中心极限定理及拆分技巧得到估计量(θn,ρn)的联合渐近分布·最后,利用ρn的结论易得Durbin-Watson统计量Dn的渐近分布.第四章,我们分别得到了估计量θn,ρn以及Durbin-Watson统计量D。的中偏差原理.首先我们由指数阶等价性定义,鞅差三角阵列的中偏差原理及拆分技巧得到估计量θn及ρn的中偏差原理,最后由ρn的结论易得Durbin-Watson统计量Dn的中偏差原理.
[Abstract]:Probability theory is a branch of mathematics that studies the statistical regularity of random phenomena. It is widely used in natural science, social science and production practice. The theory of large deviation principle has been introduced since the 1960s, which studies the convergence rate of ergodicity. Through the development of many scholars, it has been called an important branch of probability theory. It is widely used in many fields, such as partial differential, Markov process, stochastic disturbance of dynamical system, statistics, insurance and finance, etc. In the financial economy, the change process of stock price is in the form of regression model. Through the analysis of parameter estimator, the statistical law of data sequence can be studied, and the stock price can be controlled and forecasted effectively. This paper is composed of four chapters: in Chapter 1, the basic concepts of the theory of large deviation principle and the conclusions to be used are briefly reviewed, the research object and known conclusions are introduced, and then the motivation of this paper is given. In the second chapter, the model is introduced and the results obtained are given. In chapter 3, we prove the asymptotic distribution of estimator 胃 n, 蟻 n and Durbin-Watson statistic D n, respectively. Firstly, the 胃 n- 胃 n * is decomposed into the form of fraction, the asymptotic distribution of the molecule is obtained by using the central limit theorem of martingale, and the denominator converges weakly to its expectation, and the asymptotic distribution of the estimator 胃 n is obtained by Slutsky's Lemma. Secondly, the joint asymptotic distribution of the estimator (胃, 蟻 n) is obtained by using the central limit theorem of two-dimensional martingale and the split technique. Finally, the asymptotic distribution of Durbin-Watson statistic Dn is obtained easily by using the conclusion of 蟻 n. In chapter 4, we obtain the estimator 胃 n, 蟻 n and Durbin-Watson statistic D respectively. The principle of moderate deviation of First, we define the exponential order equivalence, the mid-deviation principle of martingale difference triangulation array and the split technique obtain the mid-deviation principle of the estimator 胃 _ n and 蟻 _ n. Finally, from the conclusion of 蟻 _ n, we can easily obtain the mid-deviation principle of Durbin-Watson statistic Dn.
【学位授予单位】：南京航空航天大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O211.4

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