几类金融时间序列模型统计推断

发布时间：2018-07-16 12:50

【摘要】：本文对中度偏离单位根模型的估计问题做了进一步的研究,并研究了带非平稳回归因子的变系数部分非线性模型,而且完善了非参数函数型数据局部建模回归估计的渐近性质.其一,我们得到了中度偏离单位根模型自回归系数的LAD估计量的渐近性质.给出了中度可和情形时的渐近正态分布及中度爆炸情形的柯西极限分布.其二,我们考虑了带无限方差误差项的中度偏离单位根模型的分位数回归估计.我们分别得到了中度可和情形和中度爆炸情形时分位数估计的渐近分布.模拟实验说明了当误差项方差不存在时,分位数回归估计量要比最小二乘估计量表现更好,印证了我们的理论结果.其三,我们研究了一类随机系数自回归过程当误差项方差不存在时的估计问题,并给出了估计量的一个枢轴量.模拟实验很好的验证了我们的极限理论结果.其四,我们对带非平稳回归因子的变系数部分非线性模型进行了讨论.利用拟非线性最小二乘估计,我们得到了模型中参数向量和泛函系数的估计量.在适当的条件下,我们得到了估计量的渐近性质.其中,向量参数的估计量的渐近分布依赖于模型中的非线性回归函数,而泛函系数的非参数估计量却与之无关.模拟实验很好的验证了我们的理论结果.最后,我们得到了非参数函数型数据回归局部建模估计量的渐近正态性,并利用经验似然方法构造了回归函数的逐点置信区间.模拟结果验证了我们的渐近正态性结果且说明了利用经验似然方法构造的置信区间要比基于渐近正态性构造的置信区间好.
[Abstract]:In this paper, the problem of estimating moderate deviation unit root model is further studied, and the partial nonlinear model with variable coefficients with nonstationary regression factors is studied, and the asymptotic property of regression estimation for local modeling of nonparametric functional data is improved. First, we obtain the asymptotic properties of lad estimators for the autoregressive coefficients of moderately deviated unit root models. The asymptotic normal distribution and the Cauchy limit distribution for the moderately summable case are given. Secondly, we consider the quantile regression estimation of moderate deviation unit root model with infinite variance error. We obtain the asymptotic distributions of the time division bit estimates for the moderately summable case and the moderate explosion case, respectively. The simulation results show that the quantile regression estimator performs better than the least square estimator when the variance of the error term does not exist. Thirdly, we study the estimation of a class of autoregressive processes with random coefficients when the variance of the error term does not exist, and give a pivot of the estimator. The results of our limit theory are well verified by simulation experiments. Fourthly, we discuss the partial nonlinear model of variable coefficient with nonstationary regression factor. By using the quasi-nonlinear least square estimator, we obtain the estimators of parameter vectors and functional coefficients in the model. Under suitable conditions, we obtain the asymptotic properties of the estimator. The asymptotic distribution of the estimator of vector parameter depends on the nonlinear regression function in the model, but the nonparametric estimator of the functional coefficient is independent of it. The simulation results are very good to verify our theoretical results. Finally, we obtain the asymptotic normality of the local modeling estimator of non-parametric functional data regression, and construct the point-by-point confidence interval of the regression function by using empirical likelihood method. The simulation results verify our asymptotic normality and show that the confidence interval constructed by empirical likelihood method is better than that constructed based on asymptotic normality.
【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O212.1

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