几类时间序列模型变点监测与检验

发布时间：2018-05-08 14:14

本文选题：变点监测 + 变点检验　；参考：《西北工业大学》2015年博士论文

【摘要】：时间序列模型是根据观测到的时间序列数据建立的模型,如随机系数自回归(Random coefficient autoregressive,RCA)模型,GARCH(Generalized autoregressive conditional heteroskedasticity,GARCH)模型,Logistic回归(Logistic regression)模型等,上述时间序列模型是一维数据模型,面板数据模型是同时在时间和截面上的二维数据模型.时间序列模型和面板数据模型是计量经济学研究的重要内容.在时间序列和面板数据分析中,监测和检验模型参数是否存在变点对准确建立模型和正确分析数据有重要意义.本文研究RCA(p)模型,GARCH(p,q)模型,Logistic回归模型和面板数据模型参数变点监测与检验问题.本文主要研究成果和创新点如下:(1)首次将RCA(1)(Random coefficient autoregressive model of order one)模型的参数变点监测推广到RCA(p)(Random coefficient autoregressive model of order p)模型.在原假设下给出监测统计量的渐近分布,在备择假设下证明其一致性.模拟结果表明只要选择合适的边界函数,所提方法均有较好的监测效果.数值模拟和实例分析表明了所给方法的有效性.(2)对于GARCH(p,q)模型误差项平方的分布变点监测,提出KolmogorovSmirnov型和经验特征函数型统计量.在原假设下得到两类监测统计量的渐近分布,在备择假设下证明其一致性.利用Bootstrap方法模拟经验特征函数型统计量的临界值,证明了Bootstrap方法的收敛性.数值模拟验证了方法的有效性.(3)首次将二元Logistic回归模型(Binary logistic regression model)的参数变点检验和监测推广到多元Logistic回归模型(Multinomial logistic regression model)和累积Logistic回归模型(Cumulative logistic regression model).在原假设下给出了检验和监测统计量的渐近分布,备择假设下证明了其一致性.数值模拟和实例分析表明了方法的有效性.(4)利用CUSUM方法分别研究了一般面板数据模型的方差变点检验和个体固定效应面板数据模型的系数变点检验.在原假设下证明了CUSUM型检验统计量的极限分布,在备择假设下证明了其一致性.数值模拟和实例分析验证了方法的有效性.
[Abstract]:The time series model is a model based on observed time series data, such as random coefficient autoregressive model, GARCHCHN generalized autoregressive conditional heterosed logistic regression model, and so on. The above time series model is a one-dimensional data model. Panel data model is a two-dimensional data model in both time and section. Time series model and panel data model are important contents of econometrics research. In the analysis of time series and panel data, it is very important to monitor and check whether the model parameters are changeable or not to establish the model accurately and analyze the data correctly. In this paper, we study the problem of parameter change point monitoring and checking in RCAP) model and panel data model, which are based on Logistic regression model and panel data model. The main achievements and innovations of this paper are as follows: 1) the parameter change point monitoring of RCA(1)(Random coefficient autoregressive model of order one) model is extended to RCA(p)(Random coefficient autoregressive model of order p) model for the first time. The asymptotic distribution of the monitoring statistics is given under the original hypothesis, and the consistency is proved under the alternative hypothesis. The simulation results show that the proposed method has a good monitoring effect as long as the proper boundary function is selected. Numerical simulation and example analysis show the effectiveness of the proposed method. It is shown that the KolmogorovSmirnov type and empirical eigenfunction type statistics are proposed to monitor the distribution of the square of the error term in the GARCHF / PQ model. The asymptotic distribution of two kinds of monitoring statistics is obtained under the original hypothesis, and the consistency is proved under the alternative hypothesis. The Bootstrap method is used to simulate the critical value of empirical eigenfunction statistics, and the convergence of Bootstrap method is proved. The validity of the method is verified by numerical simulation. (3) for the first time, the binary Logistic regression model is extended to multivariate Logistic regression model Multinomial logistic regression model) and cumulative Logistic regression model Cumulative logistic regression model. The asymptotic distribution of test and monitoring statistics is given under the original hypothesis, and the consistency is proved under alternative assumptions. Numerical simulation and example analysis show the effectiveness of the method. (4) using CUSUM method, the variance change point test of general panel data model and coefficient change point test of individual fixed effect panel data model are studied respectively. The limit distribution of CUSUM type test statistics is proved under the original hypothesis, and the consistency is proved under the alternative hypothesis. The effectiveness of the method is verified by numerical simulation and example analysis.
【学位授予单位】：西北工业大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：O211.61

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