金融统计监测数据的变点估计及分析

论文总字数：40090字

摘 要

时间序列模型应用在多个领域，从中分析提取有用信息至关重要。变点问题研究至此已成为统计推断中的一个非常有理论意义和前景的研究方向。

本文利用贝叶斯方法探测变点，建立时间序列模型，估计参数的先验分布，采用共轭先验分布，利用线性回归和先验信息得到相关参数值，确定后验分布和变点位置。用峰值算法减少因迭代产生的误差。利用已知变点的常数项、一次多项式、二次多项式和AR、MA、ARMA模型分别对算法进行检验，通过改变信噪比、模型类型以及模型阶数来检验算法是否能有效地找出正确的参数和阶数。

在得到变点贝叶斯估计的理论模型以后，结合江苏地区的金融监测数据：对农村、城镇居民恩格尔系数，城乡居民收入比，地区生产总值等经济时间序列数据，利用算法得到变点，结合宏观经济背景和社会发展现状，分析变点发生时的重大经济政策和其产生的效应。通过对变点的深入分析，对江苏省的区域经济增长模式，城乡收入差距，居民生活水平，产业升级，人才结构等问题都有了更深的了解。为地区经济发展提供政策导向和可行性建议。

关键词：时间序列变点 贝叶斯估计 金融监测数据

Abstract

The time series model is applied in many fields and it is very important to extract useful information from it.

The study of Change point problem has become a very theoretical and prospective research direction in statistical inference. In this paper, the Bayesian method is used to detect the change point, establish the time series model, estimate the prior distribution of parameters, use the conjugate prior distribution, use the linear regression and the prior information to obtain the correlation parameter value, and determine the posterior distribution and the change point position. The peak algorithm is used to reduce the error caused by iteration.

By using the constant term of the known change point, the first polynomial, the two polynomial model and the AR, MA and ARMA models respectively, the algorithm is tested by changing the signal-to-noise ratio, the model type and the order of the model to verify that the algorithm can effectively find the correct parameters and orders. After obtaining the theoretical model of the Variational Bayes estimation, combined with the financial monitoring data of Jiangsu region: the Engel coefficient of rural and urban residents, the income ratio of urban and rural residents, the GDP of the region, and other economic time series data, using the algorithm to get the change point, combined with the macroeconomic background and social development,to analyze the major economic policies and their effects when the change occurs. Through the analysis of the change point, we have a deeper understanding of the regional economic growth pattern, the urban-rural income disparity, the living standard, the industrial upgrading and the talent structure of Jiangsu province.According to the analysis, we canprovide policy guidance and

feasible suggestion for regional economic development.

Key Words: Time series change point Bayesian estimation financial monitoring data

目 录

摘要…………………………………………………………………………………………………………Ⅰ

Abstract……………………………………………………………………………………………… ……Ⅱ

1. 背景介绍 …………………………………………………………………………………… 1

1.1 概述 ……………………………………………………………………………1

1.2 变点问题文献综述…………………………………………………………………1

1.3 本文的主要工作………… …………………………………………………………3

1. 模型建立和算法介绍…………………………………………………………………3

2.1模型建立与符号说明 ……………………………………………………………3

2.2 变点的后验分布 ………………………………………………………………………… 5

2.3 算法参数的确定方法……………………………………………………………… 8

2.4 峰值算法……………………………………………………………………………9

第三章 模拟数据检验算法…………………………………………………………………11

3.1 多项式模型………………………………………………………………………11

3.1.1常数多项式模型…………………………………………………………11

3.1.2一次多项式模型…………………………………………………………13

3.1.3二次多项式模型…………………………………………………………16

3.2自回归模型……………………………………………………………………… 19

3.2.1 AR模型………………………………………………………………… 19

3.2.2 MA模型………………………………………………………………… 21

3.2.3 ARMA模型……………………………………………………………… 24

3.3 总结……………………………………………………………………………… 27

第四章 江苏统计监测数据的变点分析…………………………………………………… 27

4.1 农村和城镇居民恩格尔系数…………………………………………………… 27

4.2 城乡居民收入比………………………………………………………………… 35

4.3 地区生产总值，第一，第二，第三产业产值………………………………… 37

4.4 专业技术人员和工程类技术人员……………………………………………… 41

第五章 总结………………………………………………………………………………… 45

致谢………………………………………………………………………………………… 46

参考文献…………………………………………………………………………………… 47

第一章 背景介绍

1.1概述

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