【摘要】：金融市場是一個非常復(fù)雜的非線性動態(tài)系統(tǒng)。伴隨著非線性科學(xué)研究的迅猛發(fā)展,越來越多的學(xué)者運(yùn)用分形市場理論對金融市場中價格波動的非線性現(xiàn)象進(jìn)行了研究。已有的實(shí)證研究表明,金融市場呈現(xiàn)出復(fù)雜的多重分形特征。對多重分形理論進(jìn)行系統(tǒng)的研究,有助于我們進(jìn)一步加深對金融市場復(fù)雜性的認(rèn)識,揭示出金融市場復(fù)雜行為的形成機(jī)理以及動態(tài)變化規(guī)律。 本文選取上海證券綜合指數(shù)(簡稱上證綜指)和深圳證券成份指數(shù)(簡稱深證成指)1995年1月23日至2012年3月1日的每日收盤價格的股指收益數(shù)據(jù)為樣本。本文采用MFDMA方法對我國股市的多重分形特征、成因以及市場的有效性進(jìn)行了實(shí)證研究。主要包括以下幾個方面： (1)驗(yàn)證了兩序列的多重分形特征,并提出了一種改進(jìn)的指標(biāo)Ah'和△α'來衡量其多重分形程度,從而很好的實(shí)現(xiàn)了序列多重分形特征強(qiáng)度的量化。 (2)分析了形成兩序列多重分形的原因,通常認(rèn)為多重分形主要來源于序列的長程相關(guān)性和分布的重尾性。比較流行的做法是分別利用置亂數(shù)據(jù)(suffling data)法和相位隨機(jī)化的Fourier變換法來分析序列的長程相關(guān)性和分布的重尾性對多重分形的影響。然而相位隨機(jī)化的Fourier變換法(FT)是將序列的非線性結(jié)構(gòu)完全消除,而保持其線性相關(guān)性,這里的非線性性包括分布的非線性性(即重尾性)和動態(tài)的非線性性(即非線性相關(guān)性),這樣利用相位隨機(jī)化的Fourier變換法來分析分布的重尾性對多重分形的影響就不是很嚴(yán)謹(jǐn)。振幅調(diào)整的Fourier變換法(AAFT)能保持原序列的分布和線性相關(guān)性,而將非線性相關(guān)性去掉了,因此本文采用相位隨機(jī)化的Fourier變換法以及振幅調(diào)整的Fourier變換法相結(jié)合的方法來判斷分布的重尾性以及序列的非線性相關(guān)性對多重分形的影響。 結(jié)果顯示,上證綜指收益率序列的多重分形來源于分布的重尾性；而深證成指收益率序列的多重分形由序列的長程相關(guān)性和重尾分布性所致。兩序列的多重分形均不受非線性相關(guān)性的影響。因此可以說中國股市的多重分形特征來源于序列的長程相關(guān)性和分布的重尾性,而非線性相關(guān)性對其沒有影響。 (3)檢測了上海證券市場和深圳證券市場的有效性,通常認(rèn)為多重分形程度高則市場有效性程度低,這只是粗略的說法,為了更加準(zhǔn)確的判斷市場的有效性程度,本文利用多重分形情形下的有效性指標(biāo)DME對上證綜指和深證成指收益率序列的有效性進(jìn)行了實(shí)證分析。結(jié)果顯示上海證券市場的有效性程度高于深圳證券市場的有效性程度。
[Abstract]:Financial market is a very complex nonlinear dynamic system. With the rapid development of nonlinear science, more and more scholars use fractal market theory to study the nonlinear phenomenon of price fluctuation in financial market. The existing empirical studies show that the financial market presents complex multifractal characteristics. The systematic study of multifractal theory will help us to deepen our understanding of the complexity of financial market and reveal the formation mechanism and dynamic change law of complex behavior in financial market. This paper selects the Shanghai Composite Index (Shanghai Composite Index for short) and Shenzhen Securities component Index (Shenzhen Composite Index) as samples of the daily closing price from January 23, 1995 to March 1, 2012. This paper makes an empirical study on the multifractal characteristics, causes and efficiency of the stock market in China by using the MFDMA method. The main contents are as follows: (1) the multifractal characteristics of the two sequences are verified, and an improved index Ah' and 偽'is proposed to measure the multifractal degree. Thus, the quantization of multifractal feature strength of sequence is well realized. (2) the causes of multifractal of two sequences are analyzed. It is generally considered that multifractal mainly comes from the long range correlation of sequences and the heavy-tailed distribution. It is popular to use (suffling data) method of scrambling data and Fourier transform of phase randomization to analyze the influence of long range correlation and heavy-tailed distribution on multifractal. However, the phase randomization Fourier transform (FT) eliminates the nonlinear structure of the sequence completely and maintains its linear correlation. The nonlinearity here includes the nonlinearity of the distribution (that is, heavy-tailed property) and the dynamic nonlinearity (that is, the nonlinear correlation). Therefore, it is not very strict to use phase randomization Fourier transform to analyze the influence of heavy-tailed distribution on multifractal. The amplitude-adjusted Fourier transform method (AAFT) can keep the distribution of the original sequence and the linear correlation, but the nonlinear correlation is removed. In this paper, the method of phase randomization Fourier transform and amplitude-adjusted Fourier transform are used to judge the influence of the heavy-tailed distribution and the nonlinear correlation of the sequence on multifractal. The results show that the multifractal of the yield series of the Shanghai Composite Index comes from the heavy-tailed distribution, while the multifractal of the yield sequence of Shenzhen Composite Index is caused by the long range correlation and the heavy-tailed distribution of the series. The multifractal of two sequences is not affected by nonlinear correlation. Therefore, it can be said that the multifractal feature of Chinese stock market comes from the long range correlation of the series and the heavy-tailed distribution, but the nonlinear correlation has no effect on it. (3) the validity of Shanghai stock market and Shenzhen stock market is tested. It is generally considered that the degree of market efficiency is low if the multifractal degree is high. This is only a rough statement, in order to judge the validity degree of the market more accurately, In this paper, the validity of the return series of Shanghai Composite Index and Shenzhen Composite Index is empirically analyzed by using the validity index DME in the case of multifractal. The results show that the efficiency of Shanghai stock market is higher than that of Shenzhen stock market.
【學(xué)位授予單位】：山西大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：F832.51;F224

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