几类整数值自回归时间序列的建模及过程控制

发布时间：2018-05-01 00:27

本文选题：整数值时间序列 + 自回归过程　；参考：《吉林大学》2015年博士论文

【摘要】：本文主要研究几类整数值自回归时间序列的建模及过程控制问题.首先,针对具有零堆积的白相关计数数据,我们提出一种以零堆积广义幂级数分布为扰动项的一阶混合整数值自回归(ZIMINAR(1))过程,证明了该过程是唯一存在的且是严平稳遍历的,同时给出了过程的概率统计性质,研究了过程的参数估计问题.其次,我们研究了刻画不含零的自相关计数数据的零截断泊松一阶整数值自回归(ZTPINAR(1))过程,得到了该过程的高阶矩、高阶累积量以及过程跳序列的概率统计性质,同时利用联合跳控制图监控过程参数的漂移,得到较好的监控效果.最后,针对基于负二项稀疏算子建立的、以几何分布为边际分布的一阶整数值自回归(NGINAR(1))过程,我们得到了该过程跳序列的概率统计性质,并采用三种不同的控制图监控该过程参数的漂移,同时比较了三种控制图的监控效果.
[Abstract]:In this paper, the modeling and process control of several kinds of integral numerical autoregressive time series are studied. Firstly, for the white correlation counting data with zero packing, we propose a first-order mixed integer autoregressive process with zero packing generalized power series distribution as perturbation term. It is proved that the process is unique and strictly stationary ergodic. At the same time, the probabilistic and statistical properties of the process are given, and the parameter estimation problem of the process is studied. Secondly, we study the zero-truncated Poisson first order autoregressive (ZTPINARN) process, which characterizes the autocorrelation counting data without zero, and obtain the higher-order moments, the higher-order cumulants and the probability and statistical properties of the process hopping sequences. At the same time, the combined jump control chart is used to monitor the drift of process parameters, and a better monitoring effect is obtained. Finally, for the first order integral numerical autoregressive (NGINARN) process based on the negative binomial sparse operator and taking the geometric distribution as the marginal distribution, we obtain the probability and statistical properties of the jump sequence of the process. Three different control charts are used to monitor the drift of the process parameters, and the monitoring effects of the three control charts are compared.
【学位授予单位】：吉林大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：O211.61;O213.1

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