本文選題：多重分形 + 多重分形去趨勢�。� 參考：《電子科技大學》2012年博士論文

【摘要】：作為現代金融學基礎的有效市場假說(Efficient Market Hypothesis,EMH)認為市場價格反映了全部信息,市場價格的波動相互獨立且不可預測,收益率服從隨機游走假設,收益率分布服從正態(tài)或對數正態(tài)分布。但是現實中的種種金融異象意味著傳統的金融理論存在著很大的局限性,表明現實的資本市場并不如傳統理論所描述的那樣為一線性系統,而是一非線性系統。為此我們采用非線性分形理論,分析理解資本市場的基本規(guī)律。 非線性分形理論認為資本市場具有顯著的分形結構和尖峰厚尾特征,市場金融序列在一定的標度內具有持續(xù)性、反持續(xù)性,不同幅度的波動表現出多重分形特征。分形理論比傳統資本市場理論能更有效地揭示金融市場的波動本質,能更有效地揭示金融市場的基本規(guī)律。 本文借鑒分形市場理論和多重分形理論對中國創(chuàng)業(yè)板市場進行深度的分析,主要研究內容如下： (1)將多重分形方法引入到中國創(chuàng)業(yè)板市場的實證研究中,確認創(chuàng)業(yè)板指數、創(chuàng)業(yè)板行業(yè)和創(chuàng)業(yè)板上市公司時間序列的多重標度結構及多重標度特性。 (2)采用多階函數擬合方法處理中國創(chuàng)業(yè)板市場多重分形模型,使研究結果更具普遍性。 (3)利用移動時間窗的方法對中國創(chuàng)業(yè)板市場收益序列波動的多重分形特性進行研究,不僅從宏觀的角度闡述中國創(chuàng)業(yè)板市場收益序列波動的趨勢特征,還從微觀角度描述了中國創(chuàng)業(yè)板市場收益序列多重分形的特性,為探索資本市場規(guī)律提供實證依據。 (4)利用隨機化及相位隨機化思想處理中國創(chuàng)業(yè)板市場收益序列的多重分形特性,指出產生多重分形的主要原因。 (5)用多重分形去趨勢相關分析法研究創(chuàng)業(yè)板行業(yè)指數和公司間的相關關系,深度再現不同金融時間序列的相關性特征。 (6)提出并構建基于多重分形去趨勢投資組合理論,實證調整收益結果優(yōu)于中國證券投資基金的組合策略。
[Abstract]:The efficient Market hypothesis (EMH), which is the foundation of modern finance, holds that market price reflects all the information, the fluctuation of market price is independent and unpredictable, and the return rate is assumed to walk from random. Yield distribution from normal or logarithmic normal distribution. However, all kinds of financial anomalies in reality mean that the traditional financial theory has great limitations, which indicates that the real capital market is not a linear system, but a nonlinear system, as described by the traditional theory. Therefore, we use nonlinear fractal theory to analyze and understand the basic laws of capital market. The nonlinear fractal theory holds that the capital market has remarkable fractal structure and peak and thick tail characteristics, and the market financial sequence has the characteristics of persistence, anti-persistence and multi-fractal in certain scale. Fractal theory is more effective than traditional capital market theory in revealing the essence of financial market fluctuation and the basic law of financial market. This paper uses fractal market theory and multifractal theory for reference to analyze the depth of Chinese gem market. The main research contents are as follows: 1) the multifractal method is introduced into the empirical study of the gem market in China. The index of gem, the multi-scale structure and the characteristics of the time series of gem industry and gem listed companies are confirmed. 2) Multi-order function fitting method is used to deal with the multifractal model of Chinese gem market, which makes the research results more universal. 3) using the moving time window method to study the multifractal characteristics of the earnings series fluctuation in China's gem market, not only from the macro point of view, but also to explain the trend characteristics of the volatility of the growth enterprise market income series in China. It also describes the multifractal characteristics of the growth enterprise market income series in China from a micro perspective, which provides an empirical basis for exploring the laws of the capital market. 4) the multifractal characteristics of Chinese gem market income series are dealt with by using the ideas of randomization and phase randomization, and the main causes of multifractal are pointed out. 5) using multifractal detrend correlation analysis method to study the correlation between gem industry index and firms, and to reproduce the correlation characteristics of different financial time series in depth. 6) based on the multifractal detrend portfolio theory, the empirical adjustment result is better than the portfolio strategy of China's securities investment funds.
【學位授予單位】：電子科技大學
【學位級別】：博士
【學位授予年份】：2012
【分類號】：F832.51;F224

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