【作者】 孔祥凤；

【导师】 张书玲；

【作者基本信息】 西北大学 ， 基础数学， 2002， 硕士

【摘要】 中国的证券市场，特别是股票市场，以1990年12月上海证券交易所与1991年4月深圳证券交易所营业为标志，短短数年间已经得到了迅速的发展。过去对股市的研究基本建立在统计与Fourier分析的基础上，但Fourier分析不具有空间局部性。而小波变换具有良好的“自适应性”和“变焦特性”，被誉为“数学显微镜”，在处理非稳定信号上有其特殊的地位和功能。多分辨率分析就是基于此特性的一种简化空间表示方法。小波分析自80年代中后期成为一门独立的数学分支以来已在许多领域得到广泛应用，但在经济学中的应用，却还是近几年的事。本文正是基于这一背景，研究了股市信号的一些规律性——分形特性、奇异性、周期性、可预测性、有效性等，论证了小波分析在人类定量分析社会经济系统中应用的可能性。主要包括如下几方面： 1．基于股市数据无限增长及我国股市数据的时间序列不长、噪声水平较高，提出三种股市数据预处理算法，在降低噪声水平的同时又不损失长程相关的有用信息； 2．对于小波分析的奇异点检测特性进行全面的分析，提出一种基于小波分析的奇异性度量算法，并用其分析股市信号的分形特性；基于股市信号的分形特性提出一种基于小波分析及统计的奇异点检测算法； 3．利用小波分析的变焦特性研究了股市周期性，并对其成因进行分析； 4，提出了一种基于小波分析及AR模型的股市趋势预测算法； 5．根据研究结果，分析了中国股市的有效性；并对沪深股市进行了比较分析；更多还原

【Abstract】 Since the open of Shanghai Stock Exchange in December 1990 and Shenzhen Stock Exchange in March 1991, China has made a rapid development in stock market. Stock is studied mostly with statistics analysis and Fourier analysis (FA). But FA can’t analyze partly signal in tune field. Because of "self-adaptable" and "focus-adjustable", wavelet analysis (WA) is called "mathematics microscope" and plays an important role in processing the non-stationary signal. Multiresolution analysis expresses the reduced space based on the characteristics. WA has been applied in many fields since independence from mathematics in the late eighties of 20 centuries. It is in near years that WA is applied to economy. In the background,inherent laws of stock market are studied--fractal, singularity, circularity,predictability, validity. As a result, it is practicable to quantitatively analyze the system of society economy with WA. The writer of this paper aims his energy to the following questions:1. Aiming at the stock market data (SMD) increasing infinitely, being short, noised seriously, three algorithms are presented to pretreat SMD. They don’t reduce the useful information but also eliminate the noise;2. The characteristic of wavelet singularity detection is analyzed. One algorithm is introduced to measure the singularity; The fractal character of SMD is studied by the algorithm; Finally, the other algorithm is proposed to detect the singularity of SMD with WT and statistics analysis;3. The period of stock market is studied by wavelet decomposition;4. One algorithm is introduced to predict the trend of stock market with wavelet analysis and AR model;5. Finally, the validity of Chinese stock market is discussed; Shanghai stock market and Shenzhen stock market are compared;更多还原