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

【摘要】：作為現(xiàn)代金融學(xué)基礎(chǔ)的有效市場(chǎng)假說(shuō)(Efficient Market Hypothesis,EMH)認(rèn)為市場(chǎng)價(jià)格反映了全部信息,市場(chǎng)價(jià)格的波動(dòng)相互獨(dú)立且不可預(yù)測(cè),收益率服從隨機(jī)游走假設(shè),收益率分布服從正態(tài)或?qū)?shù)正態(tài)分布。但是現(xiàn)實(shí)中的種種金融異象意味著傳統(tǒng)的金融理論存在著很大的局限性,表明現(xiàn)實(shí)的資本市場(chǎng)并不如傳統(tǒng)理論所描述的那樣為一線性系統(tǒng),而是一非線性系統(tǒng)。為此我們采用非線性分形理論,分析理解資本市場(chǎng)的基本規(guī)律。 非線性分形理論認(rèn)為資本市場(chǎng)具有顯著的分形結(jié)構(gòu)和尖峰厚尾特征,市場(chǎng)金融序列在一定的標(biāo)度內(nèi)具有持續(xù)性、反持續(xù)性,不同幅度的波動(dòng)表現(xiàn)出多重分形特征。分形理論比傳統(tǒng)資本市場(chǎng)理論能更有效地揭示金融市場(chǎng)的波動(dòng)本質(zhì),能更有效地揭示金融市場(chǎng)的基本規(guī)律。 本文借鑒分形市場(chǎng)理論和多重分形理論對(duì)中國(guó)創(chuàng)業(yè)板市場(chǎng)進(jìn)行深度的分析,主要研究?jī)?nèi)容如下： (1)將多重分形方法引入到中國(guó)創(chuàng)業(yè)板市場(chǎng)的實(shí)證研究中,確認(rèn)創(chuàng)業(yè)板指數(shù)、創(chuàng)業(yè)板行業(yè)和創(chuàng)業(yè)板上市公司時(shí)間序列的多重標(biāo)度結(jié)構(gòu)及多重標(biāo)度特性。 (2)采用多階函數(shù)擬合方法處理中國(guó)創(chuàng)業(yè)板市場(chǎng)多重分形模型,使研究結(jié)果更具普遍性。 (3)利用移動(dòng)時(shí)間窗的方法對(duì)中國(guó)創(chuàng)業(yè)板市場(chǎng)收益序列波動(dòng)的多重分形特性進(jìn)行研究,不僅從宏觀的角度闡述中國(guó)創(chuàng)業(yè)板市場(chǎng)收益序列波動(dòng)的趨勢(shì)特征,還從微觀角度描述了中國(guó)創(chuàng)業(yè)板市場(chǎng)收益序列多重分形的特性,為探索資本市場(chǎng)規(guī)律提供實(shí)證依據(jù)。 (4)利用隨機(jī)化及相位隨機(jī)化思想處理中國(guó)創(chuàng)業(yè)板市場(chǎng)收益序列的多重分形特性,指出產(chǎn)生多重分形的主要原因。 (5)用多重分形去趨勢(shì)相關(guān)分析法研究創(chuàng)業(yè)板行業(yè)指數(shù)和公司間的相關(guān)關(guān)系,深度再現(xiàn)不同金融時(shí)間序列的相關(guān)性特征。 (6)提出并構(gòu)建基于多重分形去趨勢(shì)投資組合理論,實(shí)證調(diào)整收益結(jié)果優(yōu)于中國(guó)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(xué)位授予單位】：電子科技大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2012
【分類(lèi)號(hào)】：F832.51;F224

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