本文關(guān)鍵詞： 股票指數(shù) MF-DFA 單分形 多重分形 市場波動性　出處：《蘭州大學》2017年碩士論文　論文類型：學位論文

【摘要】：由于中國股市存在著大量非理性的交易者以及不完備的政策體系等因素,導致中國股市頻頻出現(xiàn)異常波動。近年來,經(jīng)過國內(nèi)外相關(guān)專家學者不斷深入的探索,認為分形理論比有效市場理論更能細致刻畫出資本市場的波動本質(zhì),同時也能更加深層次地剖析資本市場的內(nèi)在規(guī)律。因此本文運用分形理論來研究中國股市主板、中小板及創(chuàng)業(yè)板三大板塊的波動特征。本文的研究思路如下:首先對三大板塊股指收益率及成交量進行了正態(tài)性檢驗,其次,依據(jù)各板塊股指收益率和成交量這兩個指標,就各板塊股票指數(shù)依次展開了單分形和多重分形的分析,最后從橫向和縱向兩個維度,全面分析了各板塊分形特征之間的差異。本次研究的主要結(jié)論為:(1)三大板塊的日收益率時間序列均表現(xiàn)出不同程度的尖峰厚尾特性,相比于中小板及創(chuàng)業(yè)板,主板信息分布更集中,表明其易變性和波動性更為顯著,而中小板及創(chuàng)業(yè)板的信息分布相對更為均勻。(2)主板指數(shù)、中小板指數(shù)及創(chuàng)業(yè)板指數(shù)日收益率均存在顯著的長期記憶性。創(chuàng)業(yè)板的Hurst指數(shù)最低,所以創(chuàng)業(yè)板中摻雜的噪聲相對是比較少的,也即股指有更強的持續(xù)漲跌的趨勢。主板與創(chuàng)業(yè)板的Hurst指數(shù)相近,中小板的Hurst指數(shù)最高,說明中小板價格連續(xù)漲跌的趨勢不夠明顯。(3)中國股市對初始價格保持敏感且具有依賴性,遵循一個有偏的隨機過程,不服從隨機游走模型,還沒有到達弱式有效狀態(tài),是一個分形市場。(4)中國股市三大板塊收益率及成交量指標的多重分形譜均呈向右的鉤狀,說明股指收益率及成交量都呈現(xiàn)出多重分形特性,分形方法能更好地揭示中國股票市場三大板塊的波動性現(xiàn)象。
[Abstract]:Due to the existence of a large number of irrational traders and incomplete policy systems in the Chinese stock market, the Chinese stock market frequently fluctuates. In recent years, the relevant experts and scholars at home and abroad have continued to explore deeply. It is believed that fractal theory can describe the essence of capital market fluctuation more carefully than efficient market theory, and at the same time, it can analyze the inherent law of capital market more deeply. Therefore, this paper uses fractal theory to study the main board of Chinese stock market. The research ideas of this paper are as follows: firstly, the return rate and turnover of the three major stock indexes are tested normality, and secondly, according to the two indexes of stock index yield and turnover of each plate, The single-fractal and multifractal analysis of the stock index of each plate is carried out in turn, and finally, from the horizontal and vertical dimensions, The main conclusion of this study is that the time series of daily yield of the three major plates show different degree of peak and thick tail characteristics, compared with the small and medium-sized boards and the growth Enterprise Board, the main conclusion of this study is that the time series of daily yield of the three major plates show different degrees of peak and thick tail characteristics, compared with the small and medium-sized boards and the growth Enterprise Board. The information distribution of the main board is more concentrated, which indicates that the variability and volatility of the main board are more significant, while the information distribution of the small and medium-sized board and the growth enterprise board is relatively more uniform. Both the small and medium board index and the growth enterprise board index have significant long-term memory. The Hurst index of the growth enterprise board is the lowest, so the noise in the growth enterprise board is relatively less. That is, the stock index has a stronger trend of continuous rise and fall. The Hurst index of the main board is similar to that of the growth enterprise board, and the Hurst index of the small and medium-sized board is the highest. It shows that the trend of continuous rise and fall of small and medium board prices is not obvious enough) the Chinese stock market is sensitive to and dependent on the initial price, follows a biased stochastic process, does not accept the random walk model, and has not yet reached a weak effective state. It is a fractal market. (4) the multifractal spectrum of the return rate and the turnover index of the three major plates of the Chinese stock market are all hooks to the right, indicating that both the return rate of the stock index and the trading volume are multifractal. Fractal method can better reveal the volatility of the three major sectors in China's stock market.
【學位授予單位】：蘭州大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：F832.51

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