本文選題：股票市場(chǎng) + 分形市場(chǎng)��； 參考：《安徽大學(xué)》2014年碩士論文

【摘要】：對(duì)證券市場(chǎng)價(jià)格行為特征的研究一直是學(xué)術(shù)界和金融投資界中廣為關(guān)注的熱點(diǎn)問題。價(jià)格的隨機(jī)游走性和市場(chǎng)的有效性是主流金融計(jì)量理論中重要的理論基石。然而,隨著市場(chǎng)的發(fā)展,主流的有效市場(chǎng)理論不斷受到市場(chǎng)實(shí)際運(yùn)行狀況和相關(guān)研究的檢驗(yàn)。金融物理學(xué)研究中的分形理論作為研究金融市場(chǎng)較為合適的工具,能夠很大程度的彌補(bǔ)有效市場(chǎng)理論的不足。所以本文運(yùn)用分形理論,對(duì)1996年12月16日至2013年12月31日的上證指數(shù)和深證成指的市場(chǎng)特征進(jìn)行了研究,從市場(chǎng)整體的單分形特征和市場(chǎng)結(jié)構(gòu)的多重分形特征來全面的認(rèn)識(shí)市場(chǎng)。 對(duì)中國(guó)股票市場(chǎng)的單分形特征研究表明：股票市場(chǎng)是一個(gè)非線性系統(tǒng)。股價(jià)運(yùn)動(dòng)并不符合布朗運(yùn)動(dòng)和幾何布朗運(yùn)動(dòng),相比較而言,分?jǐn)?shù)布朗運(yùn)動(dòng)是股價(jià)波動(dòng)一個(gè)較好的描述。同時(shí)收益率的分布特征,并不能用正態(tài)分布很好的描述,而具有尖峰厚尾性的分形分布卻可以較好的描述收益率的分布特征。這都表明了以分形市場(chǎng)來理解股票市場(chǎng)更加符合實(shí)際情況。整體來看,中國(guó)股票市場(chǎng)具有統(tǒng)計(jì)自相似性,不同時(shí)間標(biāo)度下的價(jià)格走勢(shì)具有相似的形態(tài),不同時(shí)間標(biāo)度下的收益率具有相似的分布特征。同時(shí),R/S分析表明了中國(guó)股票市場(chǎng)是一個(gè)非有效的市場(chǎng),市場(chǎng)具有長(zhǎng)記憶性特征,以前價(jià)格波動(dòng)和歷史信息會(huì)影響以后的股價(jià)波動(dòng),因此股價(jià)在一定程度上是可以預(yù)測(cè)的。更進(jìn)一步的對(duì)長(zhǎng)記憶性的周期測(cè)度表明,平均來看,上證指數(shù)的長(zhǎng)記憶性在30天時(shí)會(huì)減少、70天時(shí)會(huì)消失,深證成指的長(zhǎng)記憶性在30天時(shí)會(huì)減少,60天時(shí)會(huì)消失。 單分形特征表明了市場(chǎng)的整體特征,進(jìn)一步的運(yùn)用多重分形理論對(duì)市場(chǎng)的結(jié)構(gòu)特征進(jìn)行研究表明：中國(guó)股市存在著多重分形結(jié)構(gòu),股價(jià)收益率的大小幅波動(dòng)之間,以及股價(jià)分布的高低價(jià)位之間具有不同的分形特征。在收益率方面,根據(jù)MF-DFA方法測(cè)得的廣義Hurst指數(shù)研究表明,中國(guó)股市大幅波動(dòng)具有反持久性特征,小幅波動(dòng)具有持久性特征,這表明了當(dāng)市場(chǎng)發(fā)生大幅波動(dòng)時(shí),有較大的概率會(huì)改變?cè)瓉淼膬r(jià)格趨勢(shì),而發(fā)生小幅波動(dòng)時(shí),有較大的概率保持原來的趨勢(shì)運(yùn)行。在股價(jià)分布方面,通過運(yùn)用多重分形譜的Holder指數(shù)、譜函數(shù)進(jìn)行研究,發(fā)現(xiàn)樣本時(shí)間內(nèi)中國(guó)股價(jià)在較高價(jià)位和較低價(jià)位的奇異性程度不同,并且得出了這種奇異性的差異與股價(jià)總體的波動(dòng)程度有關(guān),當(dāng)股價(jià)總體波動(dòng)越大,高低價(jià)位的奇異性差距就越大；同時(shí),譜函數(shù)的研究表明了樣本時(shí)間內(nèi)中國(guó)股價(jià)分布在低價(jià)位的概率較大,這是中國(guó)股市經(jīng)歷了2007年高峰后,長(zhǎng)期低迷的真實(shí)寫照。 中國(guó)股市的單分形和多重分形特征表明了股票市場(chǎng)是一個(gè)復(fù)雜的、混沌的系統(tǒng),在看似無序的市場(chǎng)中卻存在著有序的特征,市場(chǎng)的價(jià)格變化是有規(guī)律可循的。因此,從理論上說,股價(jià)在一定程度上是可以預(yù)測(cè)的。那么在實(shí)踐中,如何根據(jù)中國(guó)股市的分形特征找到有利于金融投資的有效信息,本文在此做了相關(guān)研究。 將市場(chǎng)的單分形特征與金融投資相結(jié)合,根據(jù)市場(chǎng)長(zhǎng)記憶性的突變特征,本文計(jì)算的短期移動(dòng)Hurst指數(shù)和長(zhǎng)期移動(dòng)Hurst指數(shù)的運(yùn)動(dòng)規(guī)律中,可以找到指引未來股價(jià)走勢(shì)的有效信息。這對(duì)于股市的投資實(shí)務(wù)有著重要的意義。另一方面,將市場(chǎng)的多重分形特征與金融投資相結(jié)合,通過對(duì)高頻數(shù)據(jù)的研究發(fā)現(xiàn),根據(jù)多重分形譜方法測(cè)度的市場(chǎng)Holder指數(shù)的差值△α可以作為衡量一天價(jià)格波動(dòng)幅度的指標(biāo)；同時(shí),譜函數(shù)的差值△f可以作為一天股價(jià)分布方向、分布比例情況的指標(biāo)。這對(duì)于金融投資過程中、尤其是量化投資中,對(duì)市場(chǎng)特征的量化提供了有力的參考工具。更進(jìn)一步的,把中國(guó)股市單分形、多重分形特征相結(jié)合,以分形特征的量化指標(biāo)為輸入信息,運(yùn)用滾動(dòng)的神經(jīng)網(wǎng)絡(luò)模型對(duì)模擬股市的短期走勢(shì),發(fā)現(xiàn)可以取得了較好的預(yù)測(cè)效果,這對(duì)于股票市場(chǎng)的價(jià)格預(yù)測(cè)具有現(xiàn)實(shí)意義。
[Abstract]:Study on price behavior of stock market characteristics are widely concerned hot issues in academic and financial investment community. The effectiveness of random walk and the market price is an important theoretical foundation of mainstream finance theory. However, with the development of the market, the mainstream of the efficient market theory has been testing the actual operation situation of the market and related research. The fractal theory of Finance in physics as the research of financial market more appropriate tools, can greatly compensate for the lack of effective market theory. So this paper uses the fractal theory, the market characteristics of the December 16, 1996 to December 31, 2013 Shanghai stock index and Shenzhen stock index were studied from the multi fractal characteristics of single fractal feature and market the structure of the overall market to fully understand the market.
Study on single fractal feature of the China stock market shows that the stock market is a nonlinear system. The movement of stock prices is not consistent with the Brown motion and geometric Brown motion, in comparison, fractional Brown motion stock price fluctuations a better description. The distribution characteristics and yields, and can not use the normal distribution well described description returns distribution and fractal distribution with fat tail can be better. This shows that the fractal market to understand the stock market more in line with the actual situation. Overall, China stock market price has statistical self similarity and different time scales. The trend of similar morphology with distribution characteristics similar to the different time scales of the return rate. At the same time, R/S analysis showed that the China stock market is a non effective market, the market has long memory characteristics, before the price wave Dynamic and historical information will affect the stock price volatility, the stock price can be predicted to a certain extent. Further to the long memory cycle measurement showed that on average, the long memory of the Shanghai index will be reduced in 30 days, 70 days will disappear, the long memory of Shenzhen will be reduced in 30 days, 60 days will disappear.
Single fractal characteristics show that the overall characteristics of the market, further use of structural characteristics of multi fractal theory of market research showed that Chinese stock market is a multi fractal structure, between stock return rate fluctuation, have different fractal characteristics and the distribution of shares between the high and low price. In return, according to a study the generalized Hurst index measured by MF-DFA method, China stock market volatility has anti persistent characteristics, small fluctuations in durable characteristics, this shows that when the market volatility, there is a greater probability will change the price trend of the original, and the occurrence of small fluctuations, there is a greater probability to maintain the trend in running the original. The stock price distribution, by using the multi fractal spectrum of Holder index of spectrum function, found the sample time China shares at a high price and low price The singularity degree is different, and the degree of fluctuation difference of the singularity and the overall price, when the stock price fluctuation is the overall price level, the singularity of the gap is bigger; at the same time, the research shows that the spectrum of sample time China stock distribution in large probability of low price, this is Chinese stock market experience the peak in 2007, a true portrayal of a prolonged slump.
Single fractal and multi fractal characteristics of China stock market shows that the stock market is a complex, chaotic system, in the seemingly disorderly market but there are orderly characteristics, the market price changes is to follow the law. Therefore, theoretically, the stock price can be predicted to a certain extent so. In practice, according to the fractal characteristics of China stock market find useful information for financial investment, this paper has done the related research.
The fractal characteristics and the combination of financial markets, according to the mutation characteristics of the long memory of the market, this paper calculates the movement of short-term and long-term mobile mobile Hurst index Hurst index, the effective information can be found to guide the future stock price. This has important significance for the stock market investment practice. On the other hand, the multifractal characteristics and financial markets combined, through the research on the high frequency data, according to the difference between the alpha delta method to measure the multifractal spectrum of the market Holder index could be used to measure the day price volatility index; at the same time, the difference spectrum function f can be used as a day stock price distribution, distribution ratio the index for financial investment. This process, especially quantitative investment, to quantify the characteristics of the market provides a powerful reference tool. Further, the China single stock market Combining fractal and multi fractal characteristics, we use fractal quantitative index as input information and use rolling neural network model to simulate short-term trend of stock market. We find that it can achieve better prediction effect, which has practical significance for price prediction of stock market.

【學(xué)位授予單位】：安徽大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F832.51

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