【摘要】：為了刻畫邊權(quán)網(wǎng)絡(luò)的異質(zhì)性，以及考察股票網(wǎng)絡(luò)中的異質(zhì)性與這些異質(zhì)性的來(lái)源，基于股票的距離構(gòu)建了股票網(wǎng)絡(luò)，在網(wǎng)絡(luò)結(jié)構(gòu)熵的基礎(chǔ)上給出了新概念σ-熵曲線與τ-值，，說(shuō)明了定義的合理性以及不同的網(wǎng)絡(luò)的異質(zhì)性可以由τ-值的計(jì)算結(jié)果進(jìn)行對(duì)比。越小于1的τ-值對(duì)應(yīng)的網(wǎng)絡(luò)的異質(zhì)性越大，反之越接近1對(duì)應(yīng)的網(wǎng)絡(luò)的異質(zhì)性越小。計(jì)算了具有市場(chǎng)代表性的滬深300指數(shù)與SP500指數(shù)的股票集合在不同年份的τ-值，同時(shí)為了對(duì)比行業(yè)與市場(chǎng)之間的差別，也計(jì)算了少數(shù)擁有較多公司的行業(yè)對(duì)應(yīng)的網(wǎng)絡(luò)的τ-值，比較了不同時(shí)間段不同行業(yè)與指數(shù)對(duì)應(yīng)的τ-值的大小。另一方面，基于股票集合的相關(guān)系數(shù)矩陣計(jì)算了第一特征值與對(duì)應(yīng)的第一主成分，驗(yàn)證了市場(chǎng)中存在少數(shù)經(jīng)濟(jì)因子。使用幾何布朗運(yùn)動(dòng)構(gòu)建了股票網(wǎng)絡(luò)的模型，計(jì)算了對(duì)應(yīng)的τ-值。最后針對(duì)σ-熵曲線與τ-值的概念以及性質(zhì)進(jìn)行了一些數(shù)值計(jì)算檢驗(yàn)。 本文的計(jì)算結(jié)果表明，基于股票收盤價(jià)的網(wǎng)絡(luò)對(duì)應(yīng)的τ-值均小于1，呈現(xiàn)出一定的異質(zhì)性，而單純的幾何布朗運(yùn)動(dòng)模擬出的網(wǎng)絡(luò)的τ-值等于1，沒(méi)有呈現(xiàn)出異質(zhì)性。基于τ-值與相關(guān)的主成分以及隨機(jī)矩陣?yán)碚摰姆治鼋Y(jié)果，對(duì)股票網(wǎng)絡(luò)的異質(zhì)性的來(lái)源進(jìn)行了分析，股票網(wǎng)絡(luò)存在異質(zhì)性是因?yàn)槭袌?chǎng)中的元素對(duì)信息的反應(yīng)具有異質(zhì)性，股票網(wǎng)絡(luò)的異質(zhì)性體現(xiàn)了金融市場(chǎng)的復(fù)雜性的一個(gè)方面。
[Abstract]:In order to characterize the heterogeneity of the edge weight network and investigate the heterogeneity and the source of these heterogeneity in the stock network, the stock network is constructed based on the distance of the stock. Based on the entropy of the network structure, a new concept 蟽-entropy curve and 蟿-value are given. The rationality of the definition and the heterogeneity of different networks can be compared by the calculation results of 蟿-value. The larger the heterogeneity of the network corresponding to 蟿-value less than 1, the smaller the heterogeneity of the network that is close to the corresponding value of 1. In order to compare the difference between industry and market, the 蟿-value of the corresponding network of a few industries with more companies is also calculated in order to compare the 蟿-values of the stocks of CSI 300 index and SP500 index in different years, in order to compare the differences between industries and markets. The 蟿-values of different industries and indices in different time periods are compared. On the other hand, based on the correlation coefficient matrix of stock set, the first eigenvalue and the corresponding first principal component are calculated, which verifies the existence of a few economic factors in the market. The model of stock network is constructed by using geometric Brownian motion, and the corresponding 蟿-value is calculated. Finally, the concepts and properties of 蟽 -entropy curve and 蟿 -value are tested by numerical calculation. The calculated results show that the corresponding 蟿-values of the networks based on the closing price of stocks are less than 1, showing some heterogeneity, while the 蟿-values of the networks simulated by the simple geometric Brownian motion are equal to 1, and there is no heterogeneity. Based on the analysis results of 蟿 -value and related principal components and stochastic matrix theory, the source of heterogeneity of stock network is analyzed. The heterogeneity of stock network is due to the heterogeneity of elements in the market response to information. The heterogeneity of stock network reflects the complexity of financial market.
【學(xué)位授予單位】：合肥工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：F224;F830.9

【參考文獻(xiàn)】

相關(guān)期刊論文 前5條

1 莊新田;閔志鋒;陳師陽(yáng);;上海證券市場(chǎng)的復(fù)雜網(wǎng)絡(luò)特性分析[J];東北大學(xué)學(xué)報(bào)(自然科學(xué)版);2007年07期

2 吳金閃,狄增如;從統(tǒng)計(jì)物理學(xué)看復(fù)雜網(wǎng)絡(luò)研究[J];物理學(xué)進(jìn)展;2004年01期

3 譚躍進(jìn),吳俊;網(wǎng)絡(luò)結(jié)構(gòu)熵及其在非標(biāo)度網(wǎng)絡(luò)中的應(yīng)用[J];系統(tǒng)工程理論與實(shí)踐;2004年06期

4 王林;戴冠中;胡海波;;無(wú)標(biāo)度網(wǎng)絡(luò)的一個(gè)新的拓?fù)鋮?shù)[J];系統(tǒng)工程理論與實(shí)踐;2006年06期

5 吳俊;譚躍進(jìn);鄧宏鐘;朱大智;;無(wú)標(biāo)度網(wǎng)絡(luò)拓?fù)浣Y(jié)構(gòu)非均勻性研究[J];系統(tǒng)工程理論與實(shí)踐;2007年05期

相關(guān)會(huì)議論文 前1條

1 萬(wàn)陽(yáng)松;陳忠;;加權(quán)股票網(wǎng)絡(luò)中的無(wú)標(biāo)度行為研究[A];第二屆全國(guó)復(fù)雜動(dòng)態(tài)網(wǎng)絡(luò)學(xué)術(shù)論壇論文集[C];2005年

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