【摘要】：重現(xiàn)是一個動態(tài)系統(tǒng)最基本的性質(zhì),它可以用來描述系統(tǒng)行為在相空間中的特性,研究這些特性的可視化及其分析最有力的工具就是遞歸圖。由于遞歸圖包含了系統(tǒng)所有行為的相關(guān)信息,因此本文采用基于遞歸圖的方法來研究復(fù)雜性動態(tài)系統(tǒng)內(nèi)部之間的轉(zhuǎn)化以及動態(tài)系統(tǒng)之間的相關(guān)關(guān)系,并將該方運(yùn)用到股票市場。本文首先通過基于遞歸圖和加權(quán)遞歸圖的香農(nóng)熵方法對模擬數(shù)據(jù)進(jìn)行研究,香農(nóng)熵是一種評價(jià)動態(tài)系統(tǒng)復(fù)雜性的標(biāo)準(zhǔn)方法,并且可以用來識別不同動態(tài)行為之間的變化,我們結(jié)合該方法與模擬數(shù)據(jù)來研究遞歸圖與時(shí)間序列復(fù)雜性的關(guān)系,得出加權(quán)遞歸圖的香農(nóng)熵方法可以很好的反映時(shí)間序列復(fù)雜性,即周期到混沌的轉(zhuǎn)化或者混沌到混沌的轉(zhuǎn)化,并且將該方法運(yùn)用到股票市場來探索股票指數(shù)的復(fù)雜性變化。其次,為了更加充分驗(yàn)證遞歸圖對于時(shí)間序列復(fù)雜性的分析性能,我們采用遞歸定量分析(RQA)方法進(jìn)一步說明遞歸圖研究動態(tài)系統(tǒng)復(fù)雜性變化的有效性及可靠性,遞歸定量分析能夠從更深一層角度分析系統(tǒng)內(nèi)部復(fù)雜性的變化。再次,我們提出研究不同閾值對遞歸定量分析方法的影響,我們發(fā)現(xiàn)閾值的增加會造成系統(tǒng)復(fù)雜性和穩(wěn)定性的提高。最后我們利用聯(lián)合遞歸圖(JRP)研究動態(tài)系統(tǒng)之間的相關(guān)性,聯(lián)合遞歸圖不僅可以反映兩個序列之間的關(guān)系而且能夠反映它們之間相互影響的程度,我們結(jié)合中國市場三大代表指數(shù)(SSE,SZSE,CYBZ)分析它們之間的相關(guān)性,得出SSE和CYBZ之間的相關(guān)性高于其他兩者之間。
[Abstract]:Reproduction is the most basic property of a dynamic system. It can be used to describe the behavior of the system in the phase space. The most powerful tool to study the visualization and analysis of these properties is the recursive graph. Because the recursive graph contains the information about all the behaviors of the system, this paper uses the recursive graph method to study the transformation between the complex dynamic systems and the correlation between the dynamic systems, and applies this method to the stock market. Firstly, the Shannon entropy method based on recursive graph and weighted recursive graph is used to study the simulation data. Shannon entropy is a standard method to evaluate the complexity of dynamic system, and it can be used to identify the changes between different dynamic behaviors. We study the relationship between the recursive graph and the complexity of time series by combining this method with the simulated data. It is concluded that the Shannon entropy method of weighted recursive graph can well reflect the complexity of time series. That is, the transformation from cycle to chaos or from chaos to chaos, and the method is applied to the stock market to explore the complexity of the stock index. Secondly, in order to fully verify the performance of recursive graph in analyzing the complexity of time series, we use the recursive quantitative analysis (RQA) method to further illustrate the effectiveness and reliability of recursive graph in studying the complexity change of dynamic system. Recursive quantitative analysis can analyze the complexity of the system from a deeper perspective. Thirdly, we propose to study the influence of different thresholds on the recursive quantitative analysis. We find that the increase of threshold will increase the complexity and stability of the system. Finally, we use joint recursive graph (JRP) to study the correlation between dynamic systems. Joint recursive graph can not only reflect the relationship between two sequences, but also reflect the degree of interaction between them. The correlation between SSE and CYBZ is higher than that between the other two.
【學(xué)位授予單位】：北京交通大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F224

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