股票和基金市场的多重分形分析

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摘要

目前中国已初步形成了以债券和股票为主,包含大宗商品、黄金外汇的多层次

资本市场体系.在通货膨胀的压力下,人们选择高风险高回报的产品进行投资,期望

达到货币保值甚至增值的目的.股票和基金成为大多数人投资的首选产品.众所周

知,投资存在风险,股票型基金在基金中占比增大,股票市场和基金市场的关系越来

越密切,股票和基金市场的结构是本文研究讨论的问题.

本文主要研究 2000 年后上海证券股票市场和基金市场的因果关系以及各市场

的结构,本文是一篇实证分析文章,全文共分为五章.

第一章是绪论,主要介绍选题背景及问题的提出.

第二章介绍本文选择的股票指数和基金指数,并对其进行基本统计、

Jarque-Bera 检验、Quantile-Quantile 图,并检验所选指数是否服从正态分布,结果显

示两个市场收益率序列均不服从正态分布,且均呈现尖峰厚尾.

第三章对各时间段的股票市场和基金市场因果关系进行分析.首先介绍了平稳

性检验和格兰杰因果检验模型,然后对基金市场和股票市场的格兰杰因果关系做实

证分析.通过所选的时间序列的走势图,发现相同时期的基金市场和股票市场具有

明显的同涨同跌的走势,由此推测两个市场之间可能存在因果关系.对同时期两个

市场的收益率序列进行格兰杰因果检验,结果显示股票市场的变动是引起基金市场

变动的原因,基金市场的变动不是引起股票市场变动的原因.

第四章研究股票市场和基金市场的结构.本文选用多重分形消除趋势波动分析

方法对股票市场和基金市场的结构形态进行实证分析,分析得到各序列均具有多重

分形结构,且随时间推进多重分形结构特征越来越不明显,这与市场各方面监管成

熟,风险也随之减小相符.对股票市场和基金市场对比分析得到,相同时期基金市场

的多重分形特征比股票市场的多重分形特征明显,这可能是由于基金市场与股票市

场相比不够成熟.随时间推进,基金市场逐渐成熟,相同时期股票市场的多重分形特

征比基金市场的多重分形特征明显,这可能是由于基金市场本质上比股票市场稳

定.

第五章是本文的小结.

关键词：单位根检验格兰杰因果检验多重分形分析广义赫斯特指数

ABSTRACT

At present, China has initially formed mainly in bonds and stocks, including

commodities, gold exchange multi-level capital market system. In inflation pressures

people to choose a high-risk high-return investment, expected to achieve currency hedge

or even appreciate purposes. Stocks and funds become the most preferred investment

products. As we all know, the investment risk, equity fund share of the fund increases,

the increasingly close relationship between the stock market and fund market, stock and

fund market structure and risk differences are discussed in this article.

This paper studies the causal relationship of the Shanghai stock market and fund

market after 2000 as well as the structure of the market, this paper is an empirical

analysis of the article, the text is divided into five chapters.

The first chapter is an introduction introduces the research background and issues

raised.

The second chapter describes stock index and fund index selected in this article,

and its basic statistics and Jarque-Bera test and Quantile-Quantile Figure test, whether

to follow a normal distribution, results show that the yield sequence of the two markets

are not subject to normal distribution, and showed leptokurtic.

The third chapter analyzes the causal relationship between the stock market and the

fund market at the same time period. Firstly we introduce stationary test, and Granger

causality test model, and then do empirical analysis on the fund market and the stock

market Granger causality. Though selected time series charts, the same period of the

fund market and the stock market has the same up with the down trend, which indicated

that there may be a causal relationship between the two markets, the yield on the two

markets in the same period sequence Granger causality test results show that changes in

the stock market caused the fund market movements, changes in the fund market is not

cause changes in the stock market.

The fourth chapter studies the structure of the stock market and fund market. This

selection eliminate multifractal detrended fluctuation analysis of the empirical analysis

of the stock market and the morphology of the fund market, analysis discovery each

sequence multifractal structure, and over time more and more obvious to promote

multi-fractal structure characteristics. All aspects of regulatory and market maturity, the

risk also decreases to match.The stock market and fund comparative analysis,

multifractal characteristics than the same period of the fund market is obvious the

multiple fractal characteristics of the stock market,this may be due to the fund market,

compared with the stock market is not mature enough. Advancing over time, the fund

market matures multifractal characteristics of the same period of the stock market than

the multifractal characteristics of the fund market, this may be due to the fund market is

essentially stable than the stock market.

The fifth chapter is a summary of this article.

Key Word: Unit Root Test, Granger Test, Multifractal Detrended,

Generalized Hurst Index

中文摘要

ABSTRACT

第一章绪论 ..................................................................................................................... 1

1.1 选题背景及问题的提出 ......................................................................................... 1

1.2 国内外研究现状 ..................................................................................................... 1

1.3 论文研究思路和所得结论 ..................................................................................... 3

第二章数据选择及基本统计 ......................................................................................... 4

2.1 指数简介 ................................................................................................................. 4

2.1.1 上海证券综合指数 .......................................................................................... 4

2.1.2 上海证券基金指数 .......................................................................................... 5

2.2 上证综指及基金指数对数收益率及其基本统计结果 .......................................... 6

第三章股票市场和基金市场的因果性分析 ............................................................... 14

3.1 时间序列平稳性及单位根检验 ........................................................................... 14

3.2 Granger 因果检验 ................................................................................................ 15

3.3 股票市场和基金市场的因果分析 ....................................................................... 16

3.3.1 上证综指和基金指数的平稳性检验 ............................................................ 16

3.3.2 上证综指和基金指数的格兰杰因果检验 .................................................... 17

第四章股票和基金市场的多重分形分析 ................................................................... 20

4.1 赫斯特指数简介 ................................................................................................... 20

4.2 多重分形消除趋势波动分析方法简介 ............................................................... 21

4.3 运用多重分形消除趋势波动分析方法实证分析股票和基金市场 ................... 22

4.3.1 上证综指收益率序列多重分形分析 ............................................................ 23

4.3.2 基金指数收益率序列多重分形分析 ............................................................ 24

4.3.3 上证综指和基金指数多重分形分析结果对比分析 .................................... 26

4.4 本章小结 ............................................................................................................... 28

第五章结论 ................................................................................................................... 30

附录 MF-DFA 方法计算广义 Hurst 指数的 Matlab 程序 ........................................... 31

参考文献 ......................................................................................................................... 33

在读期间公开发表的论文和承担科研项目及取得成果 ............................................. 35

致谢 ................................................................................................................................. 36

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摘要：

摘要目前中国已初步形成了以债券和股票为主,包含大宗商品、黄金外汇的多层次资本市场体系.在通货膨胀的压力下,人们选择高风险高回报的产品进行投资,期望达到货币保值甚至增值的目的.股票和基金成为大多数人投资的首选产品.众所周知,投资存在风险,股票型基金在基金中占比增大,股票市场和基金市场的关系越来越密切,股票和基金市场的结构是本文研究讨论的问题.本文主要研究2000年后上海证券股票市场和基金市场的因果关系以及各市场的结构,本文是一篇实证分析文章,全文共分为五章.第一章是绪论,主要介绍选题背景及问题的提出.第二章介绍本文选择的股票指数和基金指数,并对其进行基本统计、Jarque-Bera检验、Quan...

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