本文選題：加權(quán)分?jǐn)?shù)階排列熵 + 分?jǐn)?shù)階樣本熵�。� 參考：《北京交通大學(xué)》2017年碩士論文

【摘要】：在本篇論文中,為了探究復(fù)雜系統(tǒng)中分?jǐn)?shù)階信息熵的統(tǒng)計(jì)特性,我們通過把分?jǐn)?shù)階信息熵用于排列熵和樣本熵算法,從而將其推廣為具有分?jǐn)?shù)階形式的加權(quán)分?jǐn)?shù)階排列熵和分?jǐn)?shù)階樣本熵。文中通過不同的模擬數(shù)據(jù)和真實(shí)數(shù)據(jù)對(duì)加權(quán)分?jǐn)?shù)階排列熵和分?jǐn)?shù)階樣本熵進(jìn)行了有效性分析。實(shí)證結(jié)果表明調(diào)整分?jǐn)?shù)階數(shù)可以更靈敏和準(zhǔn)確的刻畫不同時(shí)間序列的動(dòng)態(tài)變化,這有利于描繪復(fù)雜系統(tǒng)的的動(dòng)態(tài)行為。并且本文通過數(shù)值模擬對(duì)比研究了 Potts金融模型和真實(shí)股市收益率序列的非線性復(fù)雜度行為,實(shí)證表明表明了該模型的合理性。通過結(jié)合樣本熵和復(fù)雜度不變量距離,本文提出了一種新的同步性度量方法復(fù)合復(fù)雜度同步性來刻畫兩個(gè)具有相同長(zhǎng)度的時(shí)間序列之間的同步程度。文中通過將多尺度復(fù)合復(fù)雜度同步性分析和多尺度交互樣本熵分析運(yùn)用于七只具有代表性的股票市場(chǎng)指數(shù)對(duì)比分析了不同指數(shù)對(duì)數(shù)收益率序列之間的配對(duì)行為。并且通過選取文中股票指數(shù)在相同時(shí)段內(nèi)不同采樣頻率的數(shù)據(jù)來分析數(shù)據(jù)采樣頻率對(duì)于多尺度復(fù)合復(fù)雜度同步性的影響。并且我們通過集成經(jīng)驗(yàn)?zāi)B(tài)分解方法將股票指數(shù)對(duì)數(shù)收益率序列分解為本征模函數(shù)序列并且研究分解后的序列多大程度上保留了原始序列的配對(duì)行為。實(shí)證結(jié)果證實(shí)了復(fù)合復(fù)雜度同步性的有效性并且該方法在區(qū)分時(shí)間序列之間細(xì)微的同步行為方面的優(yōu)越性。
[Abstract]:In this paper, in order to explore the statistical characteristics of fractional information entropy in complex systems, we apply fractional order information entropy to permutation entropy and sample entropy algorithm. It is generalized to weighted fractional order permutation entropy and fractional order sample entropy. In this paper, the validity of weighted fractional permutation entropy and fractional order sample entropy are analyzed by different simulation data and real data. The empirical results show that adjusting fractional order can more sensitively and accurately describe the dynamic changes of different time series, which is helpful to describe the dynamic behavior of complex systems. The nonlinear complexity behavior of Potts financial model and real stock market return series is studied by numerical simulation, and the rationality of the model is demonstrated. By combining sample entropy and complexity invariant distance, a new measure of synchronicity is proposed in this paper to describe the degree of synchronization between two time series of the same length. In this paper, multi-scale complex complexity synchronism analysis and multi-scale interactive sample entropy analysis are applied to seven representative stock market indices to compare and analyze the pairing behavior between different exponential logarithmic rate of return series. The influence of data sampling frequency on the synchronization of multi-scale composite complexity is analyzed by selecting the data of stock index in the same period of time and different sampling frequency. Furthermore, we decompose the stock exponent logarithmic return series into eigenmode function sequences by integrating empirical mode decomposition method and study the extent to which the decomposed sequences retain the pairing behavior of the original sequences. The empirical results demonstrate the effectiveness of the synchronization of complex complexity and the superiority of the proposed method in distinguishing subtle synchronization behaviors between time series.
【學(xué)位授予單位】：北京交通大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：F224

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本文編號(hào)：2082070