小波理论与经济金融时序应用研究
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摘要
小波分析以其良好的时频局域化特性,受到众多科学家和工程人员的青睐,在图像处理、模式识别、地质勘探、医学成像诊断、数值计算等各个方面都有不俗地表现。近年来,小波分析开始被引入经济与金融领域,作为处理经济金融时间序列数据的工具。但是,从目前国内外的文献来看,利用小波分析方法对实际经济金融现象进行研究分析,并充分提取其内在信息的应用相对于小波分析在其他领域的应用明显过少。本文结合经济金融时间序列特点,在探讨小波构造原理、比较与之相适宜的小波基函数和算法的基础之上,就小波分析对经济金融时序数据的处理展开研究,以期拓宽其在经济金融领域中应用的深度和广度。
从已有的自然科学各领域应用看,小波理论具有很大的潜力。小波分析在经济金融领域中的研究起步较晚,有许多方面的工作需要深入展开,本文的主要贡献所在:
(1)理论方面,对小波变换算法和小波基函数的选择进行研究。小波变换算法是小波变换得以实现的关键,本文针对经济金融时间序列的离散性特点,通过实例对几种离散小波的快速算法的实现进行了分析比较,为小波变换在经济金融领域中的应用提供方法论基础。小波基函数不仅是小波理论的重要内容,也是经济金融时间序列研究分析的前提和条件。小波基函数可从已有的小波函数中选取,也可以对已有小波函数作适当修正或重新构建新的小波函数。本文从小波构造的理论出发,分析常用的几种小波基函数的各种性能指标,通过实验的方法比较了几种小波基函数处理经济金融时间序列的效果,探讨一种或多种适合于经济金融时间序列分析计算和预测模拟的小波基函数。
(2)应用方面,对小波分析的多分辨分析原理在经济金融领域的应用展开研究。①在经济金融领域,经济现象的发展和变化不可能单独存在,必然受到多种因素、多种作用力的共同影响,而往往这些影响作用体现在不同的时间周期上,传统的单时间尺度的分析方法容易造成信息的丢失,导致分析结果不准确。本文将已在工程、水文、气象等领域得到广泛应用的小波变换的多分辨分析原理,扩展到对经济时间序列的多时间尺度分析,以探求各种因素的影响规律。②在金融领域,各种偶然因素的影响使金融时间数据中存在许多噪声,即微小不规则的干扰。这些噪声严重影响了对数据的进一步分析和处理,本文比较了传统滤波方法对金融数据去噪的缺陷,并结合金融时间序列本身的特点,以上证综合指数数据为例,探讨了小波分析对金融数据噪声消除的有效性。③将小波对金融数据的应用研究扩展到以小时、分钟、秒为间隔而采集的高频数据方面,对其体现出来的独特的“日历效应”,利用小波分析的多分辨分析原理加以分析研究,并结合ARMA模型对高频数据进行预测。
Wavelet analysis has been greatly valued by numerous scientists and engineers for its Time-Frequency localized features and been widely applied in Image Processing, Identification of Pattern, Geological Exploration, Medical Imaging diagnosis, and Numerical Calculation. It has begun to be used in the field of economy and finance to deal with the data of time series. But according to the domestic and foreign literatures, compared with other fields its application in the study and analysis of economic and financial phenomenon to fully collect their internal information is obviously too little. On the basis of the discussion of principle of wave structure and comparison of the appropriate wavelet basal function and Algorithms, the present thesis intends to research into the wave analysis of Time-Frequency data of economy and finance, while combining their characteristics, so as to widen the application of wavelet analysis in the field.
Wave analysis has great potential as far as its application in the natural science is concerned. Its use of the field of economy and finance is relatively late and therefore a lot of work needs to be furthered. The innovations of the present thesis are:
(1) In theory, the present thesis will research into algorithms of wavelet transformation and wavelet basal function. Algorithms of wavelet transformation is the key to realize wavelet transformation, so the present thesis, aiming at the discrete characteristics of economic and financial time series, also analyzes and compares the quick algorithms of several discrete wavelets with examples in order to provide methodology for the application of wavelet transformation in economy and finance. Wavelet basal function is not only an important part of wavelet analysis but also the premise and condition of time series analysis. Wavelet basal function could be chosen from the existent wavelet function, and the existent wavelet function could be properly modified or new wavelet function could be constructed. Based on the theory of wavelet construction, the present thesis analyzes and compares the performances and indexes of various wavelet functions and then tries to find out one or several wavelet functions which could be used to calculate and predict economic and financial time series analysis.
(2) In application, the present thesis also researches into the application of multi-resolution Analysis (MRA) in economy and finance. (1)In economy and finance, the development and change of economic phenomenon could not exist independently. They must be under the influence of factors and such influences are usually reflected by different periods. The traditional analysis through single measurement of time tends to cause the loss of data and therefore the result is not accurate. The present thesis extends Multi-resolution Analysis, which has been widely applied in engineering, hydrology and meteorology, to the multi-time scale analysis of economic time series in order to find out the regulations of the influence of various factors. (2)In finance, various accidental factors' influence effects lots of noises in financial time data, or minor irregular interference. The noises seriously affect the further analysis and management of the data. The present thesis compares the shortcomings of traditional Filtering Methods in noises removal from financial data and discusses, while combining the characteristics of financial time series, the validity of wavelet analysis in noises removal with data from the Shanghai Composite index. (3)The present thesis extends the application of wavelet in financial data to High Frequency Data collected with the alternation of hour, minute and second, analyzing and researching into their special Calendar Effect with the multi-resolution of wavelet analysis and predicting High Frequency Data in combination with ARMA model.
从已有的自然科学各领域应用看,小波理论具有很大的潜力。小波分析在经济金融领域中的研究起步较晚,有许多方面的工作需要深入展开,本文的主要贡献所在:
(1)理论方面,对小波变换算法和小波基函数的选择进行研究。小波变换算法是小波变换得以实现的关键,本文针对经济金融时间序列的离散性特点,通过实例对几种离散小波的快速算法的实现进行了分析比较,为小波变换在经济金融领域中的应用提供方法论基础。小波基函数不仅是小波理论的重要内容,也是经济金融时间序列研究分析的前提和条件。小波基函数可从已有的小波函数中选取,也可以对已有小波函数作适当修正或重新构建新的小波函数。本文从小波构造的理论出发,分析常用的几种小波基函数的各种性能指标,通过实验的方法比较了几种小波基函数处理经济金融时间序列的效果,探讨一种或多种适合于经济金融时间序列分析计算和预测模拟的小波基函数。
(2)应用方面,对小波分析的多分辨分析原理在经济金融领域的应用展开研究。①在经济金融领域,经济现象的发展和变化不可能单独存在,必然受到多种因素、多种作用力的共同影响,而往往这些影响作用体现在不同的时间周期上,传统的单时间尺度的分析方法容易造成信息的丢失,导致分析结果不准确。本文将已在工程、水文、气象等领域得到广泛应用的小波变换的多分辨分析原理,扩展到对经济时间序列的多时间尺度分析,以探求各种因素的影响规律。②在金融领域,各种偶然因素的影响使金融时间数据中存在许多噪声,即微小不规则的干扰。这些噪声严重影响了对数据的进一步分析和处理,本文比较了传统滤波方法对金融数据去噪的缺陷,并结合金融时间序列本身的特点,以上证综合指数数据为例,探讨了小波分析对金融数据噪声消除的有效性。③将小波对金融数据的应用研究扩展到以小时、分钟、秒为间隔而采集的高频数据方面,对其体现出来的独特的“日历效应”,利用小波分析的多分辨分析原理加以分析研究,并结合ARMA模型对高频数据进行预测。
Wavelet analysis has been greatly valued by numerous scientists and engineers for its Time-Frequency localized features and been widely applied in Image Processing, Identification of Pattern, Geological Exploration, Medical Imaging diagnosis, and Numerical Calculation. It has begun to be used in the field of economy and finance to deal with the data of time series. But according to the domestic and foreign literatures, compared with other fields its application in the study and analysis of economic and financial phenomenon to fully collect their internal information is obviously too little. On the basis of the discussion of principle of wave structure and comparison of the appropriate wavelet basal function and Algorithms, the present thesis intends to research into the wave analysis of Time-Frequency data of economy and finance, while combining their characteristics, so as to widen the application of wavelet analysis in the field.
Wave analysis has great potential as far as its application in the natural science is concerned. Its use of the field of economy and finance is relatively late and therefore a lot of work needs to be furthered. The innovations of the present thesis are:
(1) In theory, the present thesis will research into algorithms of wavelet transformation and wavelet basal function. Algorithms of wavelet transformation is the key to realize wavelet transformation, so the present thesis, aiming at the discrete characteristics of economic and financial time series, also analyzes and compares the quick algorithms of several discrete wavelets with examples in order to provide methodology for the application of wavelet transformation in economy and finance. Wavelet basal function is not only an important part of wavelet analysis but also the premise and condition of time series analysis. Wavelet basal function could be chosen from the existent wavelet function, and the existent wavelet function could be properly modified or new wavelet function could be constructed. Based on the theory of wavelet construction, the present thesis analyzes and compares the performances and indexes of various wavelet functions and then tries to find out one or several wavelet functions which could be used to calculate and predict economic and financial time series analysis.
(2) In application, the present thesis also researches into the application of multi-resolution Analysis (MRA) in economy and finance. (1)In economy and finance, the development and change of economic phenomenon could not exist independently. They must be under the influence of factors and such influences are usually reflected by different periods. The traditional analysis through single measurement of time tends to cause the loss of data and therefore the result is not accurate. The present thesis extends Multi-resolution Analysis, which has been widely applied in engineering, hydrology and meteorology, to the multi-time scale analysis of economic time series in order to find out the regulations of the influence of various factors. (2)In finance, various accidental factors' influence effects lots of noises in financial time data, or minor irregular interference. The noises seriously affect the further analysis and management of the data. The present thesis compares the shortcomings of traditional Filtering Methods in noises removal from financial data and discusses, while combining the characteristics of financial time series, the validity of wavelet analysis in noises removal with data from the Shanghai Composite index. (3)The present thesis extends the application of wavelet in financial data to High Frequency Data collected with the alternation of hour, minute and second, analyzing and researching into their special Calendar Effect with the multi-resolution of wavelet analysis and predicting High Frequency Data in combination with ARMA model.
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