小波分析在股市数据分析中的应用研究
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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；
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;
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；
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;
引文
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6． Mallat S and Hwang W L.Singularity detection and processing' with wavelet[J]. IEEE Trans.on Information Theory,1992,38(2) :617-643．
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8． Elder and Zucker.Local scale control for edge detection and blur estimation[J]. IEEE Ttans.on PAMI,1998,20(7) :699-715．
9． Chin-Hsing Chen.Wavelet Transformation for Gray-Level Corner Detection[J]. Patter Recognition,28(6) , 1995:853-859．
10． Daubechies I,Mallat S and Willky.Introduction to the special Issue[J].IEEE Trans.on Information Theory,vol 38,1992:529-532．
11． B.ALPERT.A Class of base in L2 for the sparse representation of integral opera-tor[J].SIAMJ.Math,Analysis 24(1993) .
12． T.Cooklev,M.Kato.Two-Channel multifilter bank and multiwavelet[J].Proc, ICASSP (1996) .
13． Unser M,Aldroubi,A.Eden M.On the asymptotic convergence of B Spline wavelet to Gabor function[J].IEEE Trans.on IT,1992,38(2) :864-872．
14． Guo H,pdegard J E.et al.Wavelet Based Speckle Reduction with Application to S AR Based ATD/R[J].Proc,ICIP Austin,TX,1994．
15． Donoho D L.De-Noising by Soft-Thresholding[J].IEEE Trans.on Information and Theory,1994．
16． Cvetkovic,Vetterli M.Discrete-time extrema representation:design and consist-ent reconstruction[J].IEEE Trans.on Signal Processing,1995,43(3) :81-693．
17. Evertsz,Carl J G.Fractal geometry of financial time series[J].Fractals,1995,3(3):34-35.
18．Chui C K.小波分析导论[M]．程正兴译，西安：西安交通大学出版社，1995．
19．马维祯，殷瑞祥，子波变换理论及其在信号处理中的应用[J]．数据采集及处理，1994，9(2)：121-129．
20．程俊等，小波变换用于突变检测[J]．通信学报，1995，16(3)：96-104．
21．戴善荣，数据压缩[M]．西安，西安电子科技大学出版社，1990．
22．刘贵忠，邸双亮．小波分析及其应用[M]．西安电子科技大学出版社，1992．
23．保铮，焦李成．子波理论：进展与展望[J]．电子学报，第7期，1993．
24．李强，王正志．基于小波分析的噪声抑制和数据压缩综合技术[J]．系统工程与电子技术，1998，20(12)：15-18．
25．李建平．小波分析与信号处理——理论、应用及软件实现[M]．重庆出版社，1997．
26．秦冲，商彗玲，叶耀华．利用DFT分析证券市场的周期性[J]．系统工程，1998，16(3)：33-35．
27．徐科，徐金梧，班晓娟．基于小波分解的某些非平稳时间序列预测方法[J]．电子学报，2001，29(4)：566-568．
28．向小东．子波变换极其在股市数据分析中的应用[J]．西南交通大学学报，2001，36(1)：109-112．
29．李训，沈光明．中国证券投资[M]．杭州：浙江大学出版社，1992：327-331．
30．孟卫东，严太华，丁首营．上证指数奇异信号统计检测的小波分析[J]．投资与证券，2001(5)：68-70．
31．秦前清，杨宗凯编著．实用小波分析[M]．西安：西安电子科技大学出版社，1994．
32．王哲，王春峰，顾培亮．小波分析在股票数据分析中的应用[J]．系统工程，1999，14(3)．
33．陈逢时．子波变换理论及其在信号中的应用[M]．北京：国防工业出版
34．俞禾．市场有效、周期异常与股价波动[J]．经济研究，1994(9)：43-50．
35．Arneodo A.Wavelet transform of fractals[J].第三次中法小波会议论文集，1992：87～95．
36．许沂光等．风险投资实用分析技巧[M]．中国工商联合出版社，1994．
37．王志强．混沌理论与经济学[D]．天津大学硕士学位论文，1994．
2． Daubechies I.TheWavelet transformation,time-frequency localization and signal analysis[J].IEEE Trans.on IT,1990,36(5) :961-1005．
3． Mallat S,Zhong S.Characterization of signals from multiscale edge[J].IEEE Trans.On PAMI,1992,PAMI-14 (9) :710-732．
4． Meyer Y.Wavelet:algorithms & application[M].New,York:SIA M.
5． Mallat S G.A Theory for multiresolution signal decomposition:The wavelet representation[J].IEEE Trans.on Pattern Analysis and Machine Intelligent,1989, 11(7) :674-693．
6． Mallat S and Hwang W L.Singularity detection and processing' with wavelet[J]. IEEE Trans.on Information Theory,1992,38(2) :617-643．
7． Mallat S and Zhong S.Characterization of signals from multiscale edge[J]. IEEE Trans.on Pattern and Machine Intelligence,1992,14(7) .
8． Elder and Zucker.Local scale control for edge detection and blur estimation[J]. IEEE Ttans.on PAMI,1998,20(7) :699-715．
9． Chin-Hsing Chen.Wavelet Transformation for Gray-Level Corner Detection[J]. Patter Recognition,28(6) , 1995:853-859．
10． Daubechies I,Mallat S and Willky.Introduction to the special Issue[J].IEEE Trans.on Information Theory,vol 38,1992:529-532．
11． B.ALPERT.A Class of base in L2 for the sparse representation of integral opera-tor[J].SIAMJ.Math,Analysis 24(1993) .
12． T.Cooklev,M.Kato.Two-Channel multifilter bank and multiwavelet[J].Proc, ICASSP (1996) .
13． Unser M,Aldroubi,A.Eden M.On the asymptotic convergence of B Spline wavelet to Gabor function[J].IEEE Trans.on IT,1992,38(2) :864-872．
14． Guo H,pdegard J E.et al.Wavelet Based Speckle Reduction with Application to S AR Based ATD/R[J].Proc,ICIP Austin,TX,1994．
15． Donoho D L.De-Noising by Soft-Thresholding[J].IEEE Trans.on Information and Theory,1994．
16． Cvetkovic,Vetterli M.Discrete-time extrema representation:design and consist-ent reconstruction[J].IEEE Trans.on Signal Processing,1995,43(3) :81-693．
17. Evertsz,Carl J G.Fractal geometry of financial time series[J].Fractals,1995,3(3):34-35.
18．Chui C K.小波分析导论[M]．程正兴译，西安：西安交通大学出版社，1995．
19．马维祯，殷瑞祥，子波变换理论及其在信号处理中的应用[J]．数据采集及处理，1994，9(2)：121-129．
20．程俊等，小波变换用于突变检测[J]．通信学报，1995，16(3)：96-104．
21．戴善荣，数据压缩[M]．西安，西安电子科技大学出版社，1990．
22．刘贵忠，邸双亮．小波分析及其应用[M]．西安电子科技大学出版社，1992．
23．保铮，焦李成．子波理论：进展与展望[J]．电子学报，第7期，1993．
24．李强，王正志．基于小波分析的噪声抑制和数据压缩综合技术[J]．系统工程与电子技术，1998，20(12)：15-18．
25．李建平．小波分析与信号处理——理论、应用及软件实现[M]．重庆出版社，1997．
26．秦冲，商彗玲，叶耀华．利用DFT分析证券市场的周期性[J]．系统工程，1998，16(3)：33-35．
27．徐科，徐金梧，班晓娟．基于小波分解的某些非平稳时间序列预测方法[J]．电子学报，2001，29(4)：566-568．
28．向小东．子波变换极其在股市数据分析中的应用[J]．西南交通大学学报，2001，36(1)：109-112．
29．李训，沈光明．中国证券投资[M]．杭州：浙江大学出版社，1992：327-331．
30．孟卫东，严太华，丁首营．上证指数奇异信号统计检测的小波分析[J]．投资与证券，2001(5)：68-70．
31．秦前清，杨宗凯编著．实用小波分析[M]．西安：西安电子科技大学出版社，1994．
32．王哲，王春峰，顾培亮．小波分析在股票数据分析中的应用[J]．系统工程，1999，14(3)．
33．陈逢时．子波变换理论及其在信号中的应用[M]．北京：国防工业出版
34．俞禾．市场有效、周期异常与股价波动[J]．经济研究，1994(9)：43-50．
35．Arneodo A.Wavelet transform of fractals[J].第三次中法小波会议论文集，1992：87～95．
36．许沂光等．风险投资实用分析技巧[M]．中国工商联合出版社，1994．
37．王志强．混沌理论与经济学[D]．天津大学硕士学位论文，1994．