本文關(guān)鍵詞： A股 B股 隨機(jī)矩陣 特征向量 特征值　出處：《鄭州大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：本文運(yùn)用隨機(jī)矩陣?yán)碚摰姆椒?研究經(jīng)濟(jì)異常波動(dòng)對(duì)金融股票市場的影響.文中研究選取的時(shí)間段為2007年1月4日至2009年12月31日三年的時(shí)間,研究對(duì)象為深圳證券交易所雙重上市公司A股與B股各41支股票.本文利用Pearson相關(guān)系數(shù)方法分別構(gòu)造A、B股相關(guān)系數(shù)矩陣.通過研究這些矩陣的特征值、相關(guān)系數(shù)和特征向量的統(tǒng)計(jì)性質(zhì),動(dòng)態(tài)地研究A、B股之間的異同.其動(dòng)態(tài)性具體體現(xiàn)在三個(gè)方面：一、研究A、B股的不穩(wěn)定性u(píng)(t)時(shí),選取滑動(dòng)時(shí)間窗口T=20天,每次向后滑動(dòng)19天,A、B股各產(chǎn)生38個(gè)時(shí)間段,對(duì)比分析A、B股在這些時(shí)期不穩(wěn)定性的變化情況.二、比較A、B股最大特征值λmax、平均相關(guān)系數(shù)cij及不穩(wěn)定性v(t)三者之間的關(guān)系時(shí),選取滑動(dòng)時(shí)間窗口T=100天,每次向后滑動(dòng)1天,A、B股各產(chǎn)生633個(gè)時(shí)間段,分別求出A、B股對(duì)應(yīng)633個(gè)矩陣的最大特征值和平均相關(guān)系數(shù).此時(shí)計(jì)算A、B股u(t)時(shí),所取時(shí)間窗口為T=2天,每次向后滑動(dòng)一天,共產(chǎn)生731個(gè)時(shí)間段,算出這731個(gè)時(shí)間段對(duì)應(yīng)的u(t),即每天41支股票指數(shù)不穩(wěn)定性的變化,最后把它們?nèi)弑硎驹谕粓D形中,比較三者的關(guān)系；研究特征值和平均相關(guān)系數(shù)的動(dòng)態(tài)關(guān)系時(shí),因?yàn)楣善睍r(shí)間序列長度為732天,我們?nèi)=183天,每次向后滑動(dòng)10天,共產(chǎn)生了55個(gè)時(shí)間段,對(duì)應(yīng)55個(gè)矩陣；分析相矩陣C的五個(gè)較大特征值對(duì)應(yīng)特征向量隨時(shí)間變化的穩(wěn)定性時(shí),同樣動(dòng)態(tài)地取時(shí)間窗口為T=232天,每次向后推移99天,因?yàn)锳股與B股的長度都為732,因此產(chǎn)生了5個(gè)時(shí)間段且生成5個(gè)矩陣C.三、對(duì)于A、B股分別取四個(gè)有代表性的時(shí)間段,討論在各個(gè)時(shí)間段A、B股對(duì)應(yīng)最大特征值的特征向量的分布. 最后,通過分析比較得出結(jié)論：第一、A股價(jià)格相對(duì)B股稍高,這可能是A股市場機(jī)制比較完善,投資者比較多的原因.第二、深圳證券交易所雙重上市公司A、B股股票與市場波動(dòng)有相似的運(yùn)動(dòng)趨勢,但B股反應(yīng)更敏感.第三、最大特征值與對(duì)應(yīng)最大特征值的特征向量對(duì)市場整體產(chǎn)生影響,且后者具有穩(wěn)定性.這些結(jié)論可以增強(qiáng)投資者對(duì)股市的了解,合理地分配資金,爭取減少風(fēng)險(xiǎn)增加收益.
[Abstract]:In this paper, we use the method of stochastic matrix theory to study the influence of abnormal economic fluctuations on the financial stock market. The time period chosen in this paper is from January 4th 2007 to December 31st 2009. The objects of this study are 41 A-shares and 41 B-shares of dual-listed companies in Shenzhen Stock Exchange. In this paper, the correlation coefficient matrices of A and B shares are constructed by using Pearson correlation coefficient method, and the eigenvalues of these matrices are studied. The statistical properties of correlation coefficient and eigenvector are dynamically studied in three aspects: first, when studying the instability of A and B strands, the sliding time window is chosen for 20 days. After 19 days of backward sliding, A and B stock each produce 38 time periods. The changes of instability of A and B shares in these periods are compared and analyzed. Secondly, when comparing the relationship among A, B shares maximum eigenvalue 位 max, average correlation coefficient cij and instability VT, In this paper, the maximum eigenvalue and average correlation coefficient of A and B shares corresponding to 633 matrices are obtained by selecting a sliding time window of 100 days, sliding backward for one day, and producing 633 times of B shares, respectively. When calculating A, B share UT, the time window is T ~ (2) day, and the time window is T ~ (2), respectively, when calculating A, B share UT), the maximum eigenvalue and average correlation coefficient of A and B shares are calculated respectively. A total of 731 time periods are generated by sliding backward for one day, and the changes of the instability of 41 stock indices in these 731 periods are calculated. Finally, they are expressed in the same graph, and the relationships among the three are compared. When studying the dynamic relationship between the eigenvalue and the average correlation coefficient, because the stock time series is 732 days, we take the time series T3 days and slide back 10 days each time, a total of 55 time periods are generated, corresponding to 55 matrices; When the stability of the eigenvector corresponding to the five larger eigenvalues of phase matrix C is analyzed, the time window is also dynamically selected as T ~ (232) days, each time going back for 99 days. Because the length of A shares and B shares are both 732, five time periods and five matrices C are generated. Thirdly, four representative time periods are taken for A and B shares, and the distribution of eigenvector corresponding to the maximum eigenvalue of A and B shares in each time period is discussed. Finally, the conclusion is drawn through the analysis and comparison: first, the price of A shares is slightly higher than that of B shares, which may be the reason why the mechanism of the A share market is relatively perfect and the investors are more. Second, There is a similar movement trend between A and B shares in Shenzhen Stock Exchange, but B shares are more sensitive to the reaction. Third, the maximum eigenvalue and the characteristic vector corresponding to the largest eigenvalue have an impact on the market as a whole. These conclusions can enhance investors' understanding of the stock market, allocate funds reasonably, and strive to reduce risk and increase returns.
【學(xué)位授予單位】：鄭州大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F832.51;O151.21

【共引文獻(xiàn)】

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