几类门限时间序列模型的推断研究

发布时间：2018-04-26 08:51

本文选题：门限模型 + 整数值时间序列　；参考：《吉林大学》2016年博士论文

【摘要】：本文主要研究几类门限时间序列模型的建模与统计推断问题.首先,为了刻画金融收益序列的波动性和波动的非对称性,我们提出一类带有解释变量的门限随机波动模型,利用MCMC方法对该模型的参数进行了估计,通过模拟研究了MCMC算法的精确性、敏感性和稳健性等问题,并将其应用于美国SP500股票数据的实证分析当中.其次,为了刻画整数值时间序列的非线性结构,我们基于负二项稀疏算子“*”提出一类门限整数值自回归过程,讨论了该过程的严平稳性、遍历性和矩的存在性,给出了过程参数的条件最小二乘估计和条件极大似然估计,同时给出了估计量的渐近分布.针对整数值参数的优化问题,我们给出一个基于迭代的新算法.通过数值模拟研究了估计的效果和算法的精确性,并用所提出的模型拟合了全球大地震数据.最后,我们弱化了原有SETINAR(2,1)模型的条件,重新定义了SETINAR(2,1)模型,并讨论了新模型的性质和参数的拟似然推断问题,得到了参数的极大拟似然估计和估计量的渐近分布,以及参数的置信域.通过模拟对比研究了估计的效果.并用所提出的模型拟合了一组犯罪数据.
[Abstract]:In this paper, the modeling and statistical inference of several kinds of threshold time series models are studied. Firstly, in order to characterize the volatility and asymmetry of the financial return series, we propose a threshold stochastic volatility model with explanatory variables. The parameters of the model are estimated by using MCMC method. This paper studies the accuracy, sensitivity and robustness of MCMC algorithm by simulation, and applies it to the empirical analysis of American SP500 stock data. Secondly, in order to characterize the nonlinear structure of integral numerical time series, we propose a class of threshold integral numerical autoregressive processes based on negative binomial sparse operator "*", and discuss the strict stationarity, ergodicity and moment existence of the process. The conditional least square estimation and conditional maximum likelihood estimation of process parameters are given, and the asymptotic distribution of the estimator is also given. For the optimization of integral numerical parameters, we propose a new iterative algorithm. The effect of the estimation and the accuracy of the algorithm are studied by numerical simulation, and the global seismic data are fitted with the proposed model. In the end, we weaken the condition of the original set INARA) model, redefine the set INARN 2 / 1) model, discuss the properties of the new model and the quasi-likelihood inference of the parameters, and obtain the maximum quasi-likelihood estimation of the parameters and the asymptotic distribution of the estimator. And the confidence region of the parameters. The effect of the estimation is studied by simulation and comparison. A group of crime data were fitted with the proposed model.
【学位授予单位】：吉林大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O211.61

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