【作者】 赵红强；

【导师】 石柱鲜；

【作者基本信息】 吉林大学 ， 数量经济学， 2011， 博士

【摘要】 小波分析理论作为一门新兴的数学理论和方法,已经被应用到各个领域的研究之中。近年来,国内外的学者们把小波分析方法应用在经济学上,内容包括金融学的证券市场,股票分析,期货分析等方面,也包括宏观经济周期分析,经济政策分析,产业政策分析,经济增长规律分析,市场效率分析等。小波方法将经济时间序列由单纯的相域分析扩展到了相域与频域相结合的频域-相域分析,国外将小波分析应用于经济学始于20世纪80年代中期,我国关于小波分析在经济学的应用研究始于20世纪90年代,随即发展成了一种重要的经济分析工具,得到了许多有意义的分析结论。本文在借鉴了国内外关于小波在经济学中的应用研究的基础之上,结合我国经济自身发展特点,分析了我国宏观经济的周期波动,并对我国GDP缺口进行了分析模拟,用小波神经网络对我国股票市场进行了聚类分析,对我国期货市场建立了分形协整自回归模型,总之用小波分析对我国经济运行的特征进行了分析,并得到了一些有意义的结论。全文分为七章,具体结构安排与研究结论如下：第一章,小波方法在我国经济研究的意义,介绍了本文研究的主要内容。本文主要使用了小波方法,GARCH模型,ARFIMA模型,ARMA模型,及参数,半参数,非参数估计方法。对我国GDP波动,股票债券市场,期货市场,进行了研究。第二章,小波分析与经济理论的研究综述,首先回顾了国外用小波对经济进行研究的各种经济理论与实证检验；接着,回顾了我国国内经济领域中小波的应用分析,具体包括小波在经济周期中的应用,小波在证券市场中的应用,小波在期货市场中的应用；然后回顾了小波神经网络在我国国内经济研究中的相关理论方法和研究成果以及小波方法在我国其他经济领域中的应用。第三章,介绍了小波理论的基本原理。包括小波变换,小波重构,小波分析的优点,小波包变换,双正交多分辨小波分析,小波变换与长记忆过程分析,小波分解后的时间序列的性质,谱分析,小波方差分析,分形差分过程的小波极大似然估计,小波变换下方差齐次检验,基于小波的时间序列估计,样本方差采样性质,小波神经网络,小波混沌序列分析等,以及这些理论与经济分析的联系,研究现状等。第四章,用小波方法对我国国内生产总值进行了分析及模拟。使用了单小波变换,频谱分析,高斯频谱合成法,长记忆过程模拟等方法,结合经济序列的传统分析方法,GARCH模型等。结合小波方法与GSSM方法对美国GDP非周期波动成分进行了模拟。通过对我国GDP的小波分解分析,发现我国经济波动由三个周期构成,主要为四到八个季度的短周期波动及十六到三十二个季度的中长周期波动。对我国GDP序列进行了模拟分析,该分析结合了小波频谱高斯合成法与GARCH模型,此模型对短期的预测与对长期的预测精度一样,所以非常适合于长期预测,发现未来我国经济强劲增势不会减小。其次,用小波方法测量了我国的核心通货膨胀率,实证发现,该方法优于目前计算核心通货膨胀率的几种常用方法。第五章,对我国的股票市场和投资市场进行了研究。首先得到了我国股票市场中分尺度行为的证据,然后对我国股票市场上几支股票进行了长记忆性检验,发现上证指数符合几何布朗运动,而其他几支股票的长记忆参数也非常小,在选取的几支股票中,包钢稀土的长记忆参数最大,为我国股票波动的模拟提供了依据：其次使用小波对投资市场中的一些基金的收益率进行了平滑处理和阀值分析,并对选取的几种股票型基金建立了AR-GARCH模型,得到了我国投资市场基金收益率的波动原理,利用小波神经网络对我国股票市场的安全进行了研究,发现我国股票市场安全状况整体螺旋上升;还通过将小波神经网络方法与聚类方法结合,对股票市场中投资者的信心(市场情绪)对股票市场的影响进行了研究,发现市场的心理因素是决定市场波动的重要力量,并为投资者进行股票买卖提供了一种理论方法。第六章,用小波方法对我国商品期货市场进行了分析。发现我国期货市场上的金融数据的长记忆性是非常显著的,估计了我国期货市场的长记忆参数,还用马尔科夫区制转移模型检验长记忆过程,即估计高,低两种状态,估计交易量对价格的波动是否存在影响,便利收益是影响商品期货价格的主要因素。结合小波去除噪声的计算方法,用卡吗滤波二阶段模型分别估计1-2因素模型。第七章,介绍了最新的小波理论——提升小波理论,并用提升小波对我国GDP序列进行趋势和波动分解,结合实证发现提升小波比传统小波具有更大的灵活性和可选择性。本文的创新点有结合GSSM方法与GARCH (1,1)模型对我国GDP序列进行了分析与预测；基于小波方法提出了计算我国核心通货膨胀率的一种新方法；通过小波自组织神经网络发现了我国股票市场上投资者信心对股票市场波动的影响,并提出了风险-回报率分析的一种新的方法；使用ARFIMA模型对我国期货市场进行了分析,发现便利收益是期货市场价格变动的主要因素之一；用提升小波对我国宏观经济进行了分析。由于时间的限制以及作者自身水平的局限,本文的研究难免存在较多的不足与疏漏,敬请各位专家和同仁多批评指正。更多还原

【Abstract】 Wavelet analysis theory, as a new mathematical theory and methods has been applied to various fields of study. In recent years, scholars at home and abroad applied to wavelet analysis in economics, which includes aspects of finance, macroeconomics, the economic time series analysis from a simple phase field extends to a common phase and frequency domain analysis. The wavelet analysis used in economics abroad began in the mid-20th century, the wavelet analysis used in China economics began in the recent 20 years.The first chapter, Wavelet significance of economic research in China, introduced the main contents of this paper, this paper uses the wavelet method, GARCH models, ARFIMA models, ARMA models, and parameters, semi-parametric, nonparametric estimation on China’s GDP volatility, stock and bond market, futures market, were studied.The second chapter, wavelet analysis and economic theory research summary, first reviewed the foreign economic research with wavelet various economic theories and empirical test, then, reviewed the domestic economy of the application of wavelet analysis, specifically including wavelets the application of the economic cycle, the application of wavelets in the stock market, wavelet application in the futures market, and then review the wavelet neural network in China’s domestic economic research methods and related theories of wavelet method results and other economic areas in China application.The third chapter introduces the basic principles of wavelet theory, including the wavelet transform, wavelet reconstruction, wavelet packet transform, long memory process analysis, spectrum analysis, wavelet variance analysis, wavelet neural networks, and their theoretical links with the economic analysis, economic research and so on.Chapter IV is to use wavelet method on our gross domestic product analysis and simulation, using a single wavelet transform, spectral analysis, long memory process simulation and other methods, combined with traditional methods of economic series, GARCH model. China’s economic fluctuations are mainly found in three cycles of composition, the strong growth tendency in China’s economic future will not be reduced.Chapter V of the stock market and investment markets were studied. First, the stock market has been carved-scale behavior of the evidence, and then a few of the stock market, stocks were on the long memory test and found that the Shanghai index consistent with geometric Brownian motion, and several other stocks in the long memory parameter is very small In a few selected stocks, the Baotou Rare Earth’s long memory parameter the largest fluctuation of the stock provided the basis for the simulation. Secondly, the wavelet in the investment market rate of return of some funds were smoothed and threshold analysis, and selection of several stock funds established AR-GARCH model, has been China’s investment market fund yields fluctuate principle. Wavelet neural network security in China stock market has been studied and found that the overall security situation of the stock market spiral. Through the wavelet neural network combined with the clustering method, on the confidence of investors in the stock market (market sentiment) the impact on the stock market and found that the market psychology is an important force in the decision to market fluctuations and investment by the stock trading provides a theoretical method.ChapterⅥwith the wavelet method of analysis of commodity futures markets and found that China’s futures market on the long memory of the financial data is very significant, got the estimation of the long memory parameters of the futures market, but also with a Markov regime switching model inspect long memory process, the estimated high and low status, reducing the volatility of long-term commodity; convenience yield is the impact of commodity futures prices composition’s main factor. Remove the noise wavelet method, using two-stage model of c estimate 1-2 factor models.ChapterⅦis about the latest wavelet theory-lifting wavelet theory, and with the lifting wavelet theory, got China GDP’s trends and volatility decomposition, combined with empirical evidence that the lifting wavelet is much greater in flexibility and selectivity comparing with traditional wavelet.Innovation of this paper are using the GSSM method and GARCH(1,1) model of GDP in China, stock sequences were analyzed by wavelet neural network self-organization, found that psychology factors leaven China’s stock market, propose a new method to decide when to buy and when to sail. Convenience yield is found to be the futures prices" one of the main factors.更多还原