小波分析及其对股市的分析应用

发布时间：2018-01-20 02:16

本文关键词： 小波分析奇异点周期性移动平均法小波方差及相关系数　出处：《西南财经大学》2013年硕士论文　论文类型：学位论文

【摘要】：股市是一个“高风险,高收益”的市场。如何对股市进行分析是股市存在以来众多学者力图解决的一大难题。传统的股市分析方法有移动平均线法、灰色系统法、神经网络预测法等等,它们在股市分析应用中起到了非常重要的作用。但随着股市数据量日益庞大,噪声更加繁多,变化越为频繁,这些传统分析方法对股市这样的非平稳数据进行处理有些“力不从心”。尤其是我国股市,作为一个典型的庞大但不成熟的市场,剧烈频繁的波动几乎是它的常态。傅里叶分析和统计相结合是股市研究的重要方法之一,但因为傅里叶不具备“空间局部性”,因此也束缚了它在股市中的应用。在傅里叶基础上,“小波变换”被提出。基于小波良好的“自适应性”和“变焦性”等特性,小波变换非常适合对股市这样的“非平稳数据”进行分析。本文从四个方面对小波变换在股市中的应用进行研究,并以2005年之后上海证券交易所上证综指和深圳证券交易所深证成指的每日收盘价为对象,进行实证研究,主要包括： (1)首先我们对上证综指数据进行预处理,然后利用MATLAB软件的小波工具箱,对其进行小波分解。众所周知,股市的波动一定原因是由噪声(即突变因素)造成的,因此对每层的高频分解图进行观察分析,可得出股市的奇异点,并结合李氏指数,对奇异点的突变程度进行分析。 (2)小波变换利用其分形的特性,可以将股市中的噪声信号进行剔除,从而使得股市的大趋势更加突出。通过对深证成指的每日收盘价进行小波分解和重构,得出去噪后的股市图。通过周期性分析,我们力图找出股市变动的规律性。 (3)由上知,移动平均法是主要的线性分析方法之一。但由于它具有时滞的缺陷,使得其得出的股市分析结果有些误差。基于此,我们通过研究发现,用小波变换后的低频数据,取代短期移动平均线,可有效地解决“时滞”的问题,因此本文以2005年之后招商银行的每日收盘价为研究对象,采用改进的移动平均法,进行了实证研究。 (4)上证综指和深证成指作为我国股市的两大重要指标,对它们之间的关联性进行研究,是近几年股市分析的主要方向之一。方差和相关系数是相关性研究的两个主要指标。本文结合小波变换,分别计算上证和深证数据的小波方差,及两者之间的相关系数,并对这两个指标进行分析,从而得出两市之间的关联性。
[Abstract]:The stock market is a "high risk, high yield" market. How to analyze the stock market is a big problem that many scholars have tried to solve since the stock market existed. The traditional stock market analysis method has the moving average method. Grey system method, neural network prediction method and so on, they play a very important role in the application of stock market analysis. These traditional analysis methods to deal with the non-stationary data such as the stock market is somewhat "beyond our means", especially the stock market of our country, as a typical large but immature market. Violent and frequent fluctuations are almost the norm. The combination of Fourier analysis and statistics is one of the important methods of stock market research, but because Fourier does not have "spatial localization", it also restricts its application in stock market. "Wavelet transform" is proposed, based on the good "adaptive" and "zoom" characteristics of wavelet. Wavelet transform is very suitable for the analysis of "non-stationary data" such as stock market. This paper studies the application of wavelet transform in stock market from four aspects. Taking the daily closing price of Shanghai Composite Index and Shenzhen Stock Exchange Composite Index after 2005 as the object, the empirical research is carried out, including: First, we preprocess the data of Shanghai Composite Index, then use the wavelet toolbox of MATLAB software to decompose it. The fluctuation of stock market is caused by noise (that is, sudden change factor), so the singularity of stock market can be obtained by observing and analyzing the high-frequency decomposition diagram of each layer, and combining with Li's index. The mutation degree of singularity is analyzed. Wavelet transform can eliminate the noise signal in stock market by using its fractal characteristic. In order to make the general trend of the stock market more prominent. Through wavelet decomposition and reconstruction of the daily closing price of Shenzhen Stock Exchange Index, the stock market map after noise is obtained, and the periodic analysis is carried out. We tried to find out the regularity of stock market movements. The moving average method is one of the main linear analysis methods, but because of its time delay, there are some errors in the results of stock market analysis. Based on this, we find out through the research. The problem of "delay" can be effectively solved by replacing the short-term moving average with the low-frequency data after wavelet transform. Therefore, this paper takes the daily closing price of China Merchants Bank after 2005 as the research object. An empirical study was carried out by using the improved moving average method. As two important indexes of China's stock market, the Shanghai Composite Index and the Shenzhen Composite Index are studied on the relationship between them. Variance and correlation coefficient are two main indicators of correlation research. In this paper, wavelet variance of Shanghai Stock Exchange and Shenzhen Stock Exchange data are calculated with wavelet transform. And the correlation coefficient between the two, and the analysis of the two indicators, so as to obtain the correlation between the two cities.
【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F832.51;F224

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