【作者】 李琦；

【导师】 刘三阳；

【作者基本信息】 西安电子科技大学 ， 应用数学， 2010， 硕士

【摘要】 近年来,时间序列分析方法的研究和应用飞速发展,特别在经济领域,越来越多的实际工作者开始了解并运用时间序列分析方法.随着改革的深入和经济的飞速发展,我国经济领域中存在着大量数据资料需要进行分析处理.然而在实际应用中,由于经济领域的特殊性,利用传统的频率统计方法进行经济时间序列模型分析时往往会碰到很多困难.因此,本文引入一种新的经济时间序列模型分析方法一贝叶斯分析方法.贝叶斯分析方法提供了一个更合理的经济时间序列模型分析框架.本文主要研究了向量自回归移动平均模型(VARMA)和向量分整自回归移动平均模型(VARFIMA)的贝叶斯推断理论及其应用.首先,进行了时间序列VARMA模型的贝叶斯分析,分析了时间序列VARMA( p , q)模型的统计结构及其条件似然函数,根据似然函数构造了模型参数的先验分布.研究了正态-Gamma先验分布情况下模型的贝叶斯推断理论,从统计方法上推导出预测的预报分布.利用一组用MATLAB软件模拟的二维时间序列,并利用WinBUGS进行VARMA模型仿真分析.其次,进行了多变量长记忆时间序列VARFIMA模型的贝叶斯分析.从分析VARFIMA( p , d , q)模型的统计结构开始,构建了模型的似然函数和参数的先验分布,严密地推导了模型参数的条件后验分布密度函数;利用一组用MATLAB软件模拟的二维长记忆时间序列,通过WinBUGS进行仿真分析.更多还原

【Abstract】 Recent years have witnessed wide applications of time series analysis in many fields. Particularly in the economic field, more and more practitioners have given intensive research to time series analysis methods to make full use of them. With the deepening of reform and the rapid development of economy, there is a large need for data analysis and processing in the economic field of China. However, in practical applications, due to the particularity of the economic field, the use of frequency often encounter many difficulties in traditional statistical methods for economic time series model analysis. Therefore, this thesis introduces a new model for economic time series analysis of a Bayesian analysis. Bayesian analysis methods provide a more rational analytical framework for economic time series models.The Bayesian inference theory and applications of the vector autoregressive moving average model (VARMA) and the whole sub-vector autoregressive moving average model (VARFIMA) are mainly studied.Firstly, a time series VARMA model with Bayesian methods is studied. Then the statistical structure of the model and its likelihood function are analyzed, according to the likelihood function the prior distribution of model parameters is constructed. The normal-Gamma prior distribution of Bayesian inference is studied. On the basis of the theory derived from statistical methods the distribution of the forecast is predicted. A set of two-dimensional time series simulated by MATLAB is uitilized, and the WinBUGS is used to the simulation analysis of VARMA model.Secondly, a multi-variable model of long memory time series VARFIMA Bayesian analysis is studied. On the basis of the analysis of VARFIMA (p, d, q) model of the statistical structure, the model likelihood function and parameters of the prior distribution are constructed, and then the conditions posterior distribution density function of the model parameters are derived with high precision. A set of two-dimensional time series simulated by MATLAB is utilized, and the WinBUGS is used to the simulation analysis of VARFIMA model.更多还原