主成分分析及因子分析在股指中的应用

论文编号:XXLW065 论文字数:11211,页数:24

摘     要

 股价指数一直以来被称为国民经济的晴雨表。近年来,我国证券市场发展迅速，指数化投资规模日益扩大,但股价指数的开发相对滞后，投资者对指数缺乏深刻认识，限制了指数型产品的创新。因此,对股价指数进行定量分析显得尤其重要。很多机构在编制股价指数时，常常把成分股纳入四大分类指数：金融指数、地产指数、工商指数和公用指数。本文通过对这四大指数进行主成分分析、因子分析，来判断不同时期股价指数的整体情况，再采用协整分析法来表明各股价指数间的均衡关系。
 主成分分析是将多个指标化为少数指标的一种统计方法。本文首先对四大指数进行主成分分析，在SPSS主成分分析结果中，可以看出，累计贡献率在95.485%的特征值有两个,即前两个主成分已经表达四大指数所反应的信息。通过初始因子载荷矩阵可以计算出两个主成分的特征向量,从而得到这两个主成分的表达式。
 在对四大指数进行因子分析时，采用方差极大化正交旋转,确定了两个具有经济意义的公因子：基本上支配了金融、地产、工商三大指数的盈利因子和基本上支配了公用指数的公用因子。根据主成分的得分系数矩阵,可以得到股价指数的因子得分模型,以表明各个主成分的评价得分。进行因子分析后,由因子得分和各因子的方差贡献率的比重作为权重进行加权汇总,得出各时段股价指数的综合得分表达式。
 在研究时间序列之间的关系时，对明显的非平稳序列之间做回归，将会出现错误的结论即“伪回归”问题，本文采用协整分析法来确定非平稳时间序列之间的关系。首先对四大股价指数进行单位根检验，得出四大指数都是一阶单整序列。再采用最小二乘法进行协整检验，因为检验的残差序列具有平稳性，因此，四大股价指数之间是协整的，即它们之间存在长期均衡关系。

关键词：主成分分析  因子分析  协整分析

Abstract
 Stock price index has always been playing the role of barometer of national economy. In recent years, with the rapid development of securities market, the scale of investment is getting larger. However, the innovation process of index products is still restricted because of comparable slow development of stock price index and inventors’ inadequate knowledge about index. Therefore, quantitative analysis upon stock price index is very vital and indispensible. Many institutions take component-shares as one of the four indices which are financial index, estate index, commercial index and public index. This paper aims to figure out the general situations of stock price index during different periods by analyzing both main components and factors of the four indices. Then shows the balance relations among stock price indices by using Co-integration analytical method.
 Main-component analysis is a statistic method that changes several indices into fewer indices. In this paper, main-component analysis of the four indices will firstly be given. From the main-component analysis results of SPSS, we can see there are two eigenvalue whose accumulate contribution rates are at 95.485%, which means former two main components have already indicate all information that the four indices want to show. And expressions of the two components can be worked out after knowing their eigenvectors which may be gained through original gene-load matrix.
 When analyze the factors of the four indices, we will obtain two common factors which owns economical effects by the means of variance maximum orthogonal rotation. One is a profitable factor that basically dominates financial index, estate index and commercial index, three of the four indices. The other is a common factor that basically controls the public index. According to the main-component scoring coefficient matrix, we can get the factor scoring model of stock price index so as to show evaluating score of separate main component. After the analysis towards factors, taking the proportion of factor scoring and separate variance contribution rate as standard to evaluate generally, we can finally figure out a general scoring expression of stock price index during every period.
 During the process of research the relation between time sequences, making regresses between apparent unstable sequences will be ended up wrong conclusion, which might be “false regress”. This paper adopts Co-integration analytical method to assure the connections between unstable sequences. First of all, make an inspection towards unit roots of the four stock price indices in order to prove that they are all Integration Process sequences. Then make full use of least-two multiplication to Co-integration inspection. For those inspected residual sequences boast stability, the four stock price indices are Co-integrated. That is to say that there are long-term balanced relations among them.

Keywords：Principal component analysis; Factor Analysis; Co-integration

目  录
摘  要 1
Abstract 2
目  录 4
第一章  绪论 1
1.1  研究动机和目的 1
1.2  研究的背景 1
1.2.1 股价指数发展现状 1
1.2.2 股指的分类和功能 2
1.2.3 我国的指数体系 2
1.2.4 我国股价指数在指数化投资中的应用 2
1.3  研究方法与系统描述 3
1.3.1 主成分分析法 3
1.3.2 因子分析法 3
1.3.3 协整分析 4
1.4  论文内容概述 4
第二章  主成分分析 5
2.1  主成分分析法 5
2.1.1 主成分分析法的定义 5
2.1.2 主分成分析原理 5
2.1.3 主成分分析数学模型 5
2.1.4 进行主成分分析主要步骤如下： 6
2.2  主成分分析法关于股指联系的实例研究 6
2.2.1 变量与数据的选取 6
2.2.2 结合SPSS的运行结果进行主成分分析 6
第三章  因子分析 9
3.1  因子分析法 9
3.1.1 因子分析的定义 9
3.1.2 因子分析的原理 9
3.1.3 因子分析数学模型 9
3.1.4 行主成分分析主要步骤如下： 10
3.2  因子分析法关于股指联系的实例研究 10
第四章  协整分析 13
4.1  伪回归 13
4.2  协整分析法 14
4.2.1 单位根过程 14
4.2.2 协整(Cointegration)过程 15
4.3  协整分析法关于股指联系的实例研究 15
4.3.1 单位根检验 15
4.3.2 协整分析 16
第五章  结论 17
致  谢 18
参考文献 19