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

【摘要】：對證券市場價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)注的熱點問題。價格的隨機游走性和市場的有效性是主流金融計量理論中重要的理論基石。然而,隨著市場的發(fā)展,主流的有效市場理論不斷受到市場實際運行狀況和相關(guān)研究的檢驗。金融物理學(xué)研究中的分形理論作為研究金融市場較為合適的工具,能夠很大程度的彌補有效市場理論的不足。所以本文運用分形理論,對1996年12月16日至2013年12月31日的上證指數(shù)和深證成指的市場特征進行了研究,從市場整體的單分形特征和市場結(jié)構(gòu)的多重分形特征來全面的認識市場。 對中國股票市場的單分形特征研究表明：股票市場是一個非線性系統(tǒng)。股價運動并不符合布朗運動和幾何布朗運動,相比較而言,分數(shù)布朗運動是股價波動一個較好的描述。同時收益率的分布特征,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來理解股票市場更加符合實際情況。整體來看,中國股票市場具有統(tǒng)計自相似性,不同時間標(biāo)度下的價格走勢具有相似的形態(tài),不同時間標(biāo)度下的收益率具有相似的分布特征。同時,R/S分析表明了中國股票市場是一個非有效的市場,市場具有長記憶性特征,以前價格波動和歷史信息會影響以后的股價波動,因此股價在一定程度上是可以預(yù)測的。更進一步的對長記憶性的周期測度表明,平均來看,上證指數(shù)的長記憶性在30天時會減少、70天時會消失,深證成指的長記憶性在30天時會減少,60天時會消失。 單分形特征表明了市場的整體特征,進一步的運用多重分形理論對市場的結(jié)構(gòu)特征進行研究表明：中國股市存在著多重分形結(jié)構(gòu),股價收益率的大小幅波動之間,以及股價分布的高低價位之間具有不同的分形特征。在收益率方面,根據(jù)MF-DFA方法測得的廣義Hurst指數(shù)研究表明,中國股市大幅波動具有反持久性特征,小幅波動具有持久性特征,這表明了當(dāng)市場發(fā)生大幅波動時,有較大的概率會改變原來的價格趨勢,而發(fā)生小幅波動時,有較大的概率保持原來的趨勢運行。在股價分布方面,通過運用多重分形譜的Holder指數(shù)、譜函數(shù)進行研究,發(fā)現(xiàn)樣本時間內(nèi)中國股價在較高價位和較低價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總體的波動程度有關(guān),當(dāng)股價總體波動越大,高低價位的奇異性差距就越大；同時,譜函數(shù)的研究表明了樣本時間內(nèi)中國股價分布在低價位的概率較大,這是中國股市經(jīng)歷了2007年高峰后,長期低迷的真實寫照。 中國股市的單分形和多重分形特征表明了股票市場是一個復(fù)雜的、混沌的系統(tǒng),在看似無序的市場中卻存在著有序的特征,市場的價格變化是有規(guī)律可循的。因此,從理論上說,股價在一定程度上是可以預(yù)測的。那么在實踐中,如何根據(jù)中國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。 將市場的單分形特征與金融投資相結(jié)合,根據(jù)市場長記憶性的突變特征,本文計算的短期移動Hurst指數(shù)和長期移動Hurst指數(shù)的運動規(guī)律中,可以找到指引未來股價走勢的有效信息。這對于股市的投資實務(wù)有著重要的意義。另一方面,將市場的多重分形特征與金融投資相結(jié)合,通過對高頻數(shù)據(jù)的研究發(fā)現(xiàn),根據(jù)多重分形譜方法測度的市場Holder指數(shù)的差值△α可以作為衡量一天價格波動幅度的指標(biāo)；同時,譜函數(shù)的差值△f可以作為一天股價分布方向、分布比例情況的指標(biāo)。這對于金融投資過程中、尤其是量化投資中,對市場特征的量化提供了有力的參考工具。更進一步的,把中國股市單分形、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,運用滾動的神經(jīng)網(wǎng)絡(luò)模型對模擬股市的短期走勢,發(fā)現(xiàn)可以取得了較好的預(yù)測效果,這對于股票市場的價格預(yù)測具有現(xiàn)實意義。
[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)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：F832.51

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