部分线性ARCH误差模型的经验似然方法研究

发布时间：2018-05-16 16:30

本文选题：经验似然 + 渐近正态　；参考：《中国矿业大学》2015年硕士论文

【摘要】：经验似然方法是由Owen提出的一种非参数统计推断方法,具有良好的渐近性质,如何将这种方法用于部分线性ARCH误差模型的统计推断是一个热点的问题.虽然文献中利用最大似然估计的方法构造了经验似然统计量,但要求误差项的四阶矩有限,这个要求一般对金融时间序列过于苛刻.因此,本文利用最小绝对偏差(LAD)估计方法构造经验似然统计量,在误差项是厚尾分布的情况下,分别推导出LAD估计量和经验似然比统计量的渐近性质.最后,本文进行了蒙特卡罗模拟,模拟出这两种方法的置信区域的覆盖率,根据模拟所得到的结果比较了这两种方法的优越性.具体做了以下几个方面的工作:第一,对部分线性ARCH误差模型,构造参数的目标函数,然后求目标函数的最小值,得到LAD估计量;第二,根据鞅的中心极限定理和遍历性定理,证明了LAD估计量的渐近正态性,并且给出了渐近正态置信区域;第三,在LAD估计的基础上,构造了经验似然比统计量,然后了证明经验似然比统计量的渐近性质,并且给出了经验似然置信区域;第四,进行数据模拟,计算置信区域的覆盖率,通过进行对比,得出经验似然方法具有更好的优越性.
[Abstract]:Empirical likelihood method is a nonparametric statistical inference method proposed by Owen. It has good asymptotic property. How to apply this method to the statistical inference of partial linear ARCH error model is a hot issue. Although the empirical likelihood statistics are constructed by using the method of maximum likelihood estimation in the literature, the fourth order moment of the error term is limited, which is generally too harsh for the financial time series. In this paper, the empirical likelihood statistics are constructed by using the method of minimum absolute deviation (lad) estimation. The asymptotic properties of the LAD estimator and the empirical likelihood ratio statistic are derived under the condition that the error term is a thick-tailed distribution. Finally, Monte Carlo simulation is carried out to simulate the confidence region coverage of the two methods, and the advantages of the two methods are compared according to the simulation results. The main work is as follows: firstly, the objective function of parameter is constructed for partial linear ARCH error model, then the minimum value of objective function is obtained, and the LAD estimator is obtained. Secondly, according to the central limit theorem and ergodicity theorem of martingale, The asymptotic normality of LAD estimator is proved, and the asymptotic normal confidence region is given. Thirdly, on the basis of LAD estimation, empirical likelihood ratio statistics are constructed, and the asymptotic properties of empirical likelihood ratio statistics are proved. And the empirical likelihood confidence region is given. Fourth, the data simulation, the calculation of confidence region coverage, through comparison, it is concluded that empirical likelihood method has better advantages.
【学位授予单位】：中国矿业大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O212.1

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