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題名 股票群的隨機行走模型與內在結構 - 以1996-1999年美國股票S&P500為例之初步分析
Random walk model and underlying structure - a primitive study of collections of US stocks over 1996-1999
作者 黃鈺峰
Huang, Yu Feng
貢獻者 馬文忠
Wen Jong Ma
黃鈺峰
Huang, Yu Feng
關鍵詞 相關矩陣
隨機矩陣定理
耦合隨機行走
最小展開樹
correlation matrix
random matrix theorem
coupled random walk
minimum spanning tree
日期 2012
上傳時間 11-Jul-2013 17:54:17 (UTC+8)
摘要 我們從計算股價的相關矩陣，然後利用隨機矩陣定理的結果，了解到股票市場並非符合隨機過程的預測，進而得知股票對股票之間具有關聯性，然其長時距下股票價格對數報酬的變化會呈現隨機行走的模式，因此我們對其結果提出二種不同的耦合隨機行走模型，試圖闡釋股票市場間的關聯性可融合到耦合隨機行走模型之中，並藉由均方對數報酬(mean square log-return，MSLR)來探討此事情。
最後，為了瞭解關聯性的關係，並利用其來了解股票市場內部結構的特性，因此我們利用股價的相關矩陣來建構最小展開樹進行分析，發現當時間尺度越大其圖形越密集，中心幾乎為「GE」這家公司，因此其股票市場具有一定的判斷指標。
By means of calculating the correlation matrix of the price of stock and using the results of random matrix theorems，we learned that the stock market does not match the prediction of stochastic processes and the stock-stock is correlated。However，stock’s price log-return changes under long time scale will appear random walk model. Therefore，we propose two kinds of the different coupled random walk model，that try to explain the correlation between the stock markets can be integrated into the coupled random walk model，and using the mean square log-return( MSLR) to investigate this issue。
Finally，to understand the relationship of correlation matrix and by using it to know the characteristics of the underlying structure of the stock market，we use the correlation matrix of the price to construct the minimum spanning tree for analysis。The results showed that when the time scale is greater, the graphics are more intensive，and the center is almost the same company，"GE"， indicating that the stock market has a certain judgment index。
參考文獻 [1] R. Engle, J. Econometrics 100, 53 (2001)
[2] 以隨機行走模息來解讀股票間的關聯性 馬文忠/胡進錕 物理雙月刊2008.6
[3] L.Laloux,P.Cizeau,J.-P.Bouchaud and M.Potters,Phys. Rev. Lett. 83, 1467 (1999).
[4] V. Plerou et al., Phys. Rev. Lett. 83, 1471 (1999)
[5] J. D. Noh, Phys. Rev. E 61, 5981 (2000).
[6] W. J. Ma, C. K. Hu and R. E. Amritkar, Phys. Rev.E 70, 026101 (2004)
[7] Ma,Wang,Chen and Hu Crossover behavior of stock returns and mean square
displacements of particles governed by the Langevin equation(2013)
[8] A. Einstein, Ann. Phys. (Leipzig) 17, 549 (1905).
[9] 數學傳播第九卷第三期 漫談布朗運動-----李育嘉
[10] L. Bachelier, Ann. Sci. Ecole Norm. Sup. s`erie 3,17, 21 (1900)
[11] 財務統計 傅承德 中央研究院統計科學研究所
[12] Cowles, A. (1933). Can stock market forecasters forecast?Econometrica,309-324.
[13] Cowles, A. and John, H. E. (1937). Some a posteriori probabilities in stock market action. Econometrica, 5, 280-294
[14] Working, H. (1934). A random-difference series for use in the analysis of time series. Journal of the American Statistical Association, 29, 11-24
[15] Kendall, M. G. (1953). The analysis of economic time-series. Part 1. Prices. J ournal of the Royal Statistical Society, 96, 11-25
[16] A first course in probability / Sheldon Ross
[17] J. P. Bouchaud,M. Potters,Theory of Financial Risks second reprint
[18] 論數學遊戲 張維忠 數學傳播 30卷4期, pp. 83-94
[19] Van Den Heuvel, M., Mandl, R., & Pol, H. H. (2008). Normalized cut group clustering of resting-state FMRI data. PLoS One, 3(4), e2001.
[20] Albert-László Barabási & Réka Albert (October 1999). "Emergence of scaling in random networks". Science 286 (5439): 509–512
[21] R. C. Prim: Shortest connection networks and some generalizations. In: Bell System Technical Journal, 36 (1957), pp. 1389–1401
[22] Joseph. B. Kruskal: On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem. In: Proceedings of the American Mathematical Society, Vol 7, No. 1 (Feb, 1956), pp. 48–50
[23] Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms, Second Edition. MIT Press and McGraw-Hill, 2001. ISBN 0-262-03293-7. Section 23.2: The algorithms of Kruskal and Prim, pp. 567–574.
[24] R. N. Mantegna,Eur. Phys. J. B. 11, 193–197, (1999)
[25] PEDRO J. BALLESTER, W. GRAHAM RICHARDS Vol. 28, No. 10 .Journal of Computational Chemistry
描述 碩士
國立政治大學
應用物理研究所
100755001
101
資料來源 http://thesis.lib.nccu.edu.tw/record/#G1007550011
資料類型 thesis
dc.contributor.advisor 馬文忠zh_TW
dc.contributor.advisor Wen Jong Maen_US
dc.contributor.author (Authors) 黃鈺峰zh_TW
dc.contributor.author (Authors) Huang, Yu Fengen_US
dc.creator (作者) 黃鈺峰zh_TW
dc.creator (作者) Huang, Yu Fengen_US
dc.date (日期) 2012en_US
dc.date.accessioned 11-Jul-2013 17:54:17 (UTC+8)-
dc.date.available 11-Jul-2013 17:54:17 (UTC+8)-
dc.date.issued (上傳時間) 11-Jul-2013 17:54:17 (UTC+8)-
dc.identifier (Other Identifiers) G1007550011en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/58852-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用物理研究所zh_TW
dc.description (描述) 100755001zh_TW
dc.description (描述) 101zh_TW
dc.description.abstract (摘要) 我們從計算股價的相關矩陣，然後利用隨機矩陣定理的結果，了解到股票市場並非符合隨機過程的預測，進而得知股票對股票之間具有關聯性，然其長時距下股票價格對數報酬的變化會呈現隨機行走的模式，因此我們對其結果提出二種不同的耦合隨機行走模型，試圖闡釋股票市場間的關聯性可融合到耦合隨機行走模型之中，並藉由均方對數報酬(mean square log-return，MSLR)來探討此事情。
最後，為了瞭解關聯性的關係，並利用其來了解股票市場內部結構的特性，因此我們利用股價的相關矩陣來建構最小展開樹進行分析，發現當時間尺度越大其圖形越密集，中心幾乎為「GE」這家公司，因此其股票市場具有一定的判斷指標。		zh_TW
dc.description.abstract (摘要) By means of calculating the correlation matrix of the price of stock and using the results of random matrix theorems，we learned that the stock market does not match the prediction of stochastic processes and the stock-stock is correlated。However，stock’s price log-return changes under long time scale will appear random walk model. Therefore，we propose two kinds of the different coupled random walk model，that try to explain the correlation between the stock markets can be integrated into the coupled random walk model，and using the mean square log-return( MSLR) to investigate this issue。
Finally，to understand the relationship of correlation matrix and by using it to know the characteristics of the underlying structure of the stock market，we use the correlation matrix of the price to construct the minimum spanning tree for analysis。The results showed that when the time scale is greater, the graphics are more intensive，and the center is almost the same company，"GE"， indicating that the stock market has a certain judgment index。		en_US
dc.description.tableofcontents 摘要 1
Abstract 2
Chapter 1 簡介 4
Chapter 2 理論與方法 8
2.1 隨機行走簡介 8
2.2 一維隨機行走 12
2.3 隨機矩陣理論 17
2.3.1 Wishart matrix 特徵值分布 17
2.4 耦合隨機行走 18
2.4.1 耦合隨機行走模型I 18
2.4.2 耦合隨機行走模型II 20
2.5 網路介紹 23
2.5.1無尺度網路 25
2.5.2 BA模型 26
2.5.3最小展開樹模型 30
Chapter 3 實證分析 35
3.1相關矩陣之特徵值分布 35
3.2耦合隨機行走模型 37
3.2.1耦合隨機行走模型I 37
3.2.2耦合隨機行走模型II 41
3.3最小展開樹圖形的定量性分析 43
Chapter 4 結論 62
文獻參考 64		zh_TW
dc.format.extent 1989574 bytes-
dc.format.mimetype application/pdf-
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G1007550011en_US
dc.subject (關鍵詞) 相關矩陣zh_TW
dc.subject (關鍵詞) 隨機矩陣定理zh_TW
dc.subject (關鍵詞) 耦合隨機行走zh_TW
dc.subject (關鍵詞) 最小展開樹zh_TW
dc.subject (關鍵詞) correlation matrixen_US
dc.subject (關鍵詞) random matrix theoremen_US
dc.subject (關鍵詞) coupled random walken_US
dc.subject (關鍵詞) minimum spanning treeen_US
dc.title (題名) 股票群的隨機行走模型與內在結構 - 以1996-1999年美國股票S&P500為例之初步分析zh_TW
dc.title (題名) Random walk model and underlying structure - a primitive study of collections of US stocks over 1996-1999en_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) [1] R. Engle, J. Econometrics 100, 53 (2001)
[2] 以隨機行走模息來解讀股票間的關聯性 馬文忠/胡進錕 物理雙月刊2008.6
[3] L.Laloux,P.Cizeau,J.-P.Bouchaud and M.Potters,Phys. Rev. Lett. 83, 1467 (1999).
[4] V. Plerou et al., Phys. Rev. Lett. 83, 1471 (1999)
[5] J. D. Noh, Phys. Rev. E 61, 5981 (2000).
[6] W. J. Ma, C. K. Hu and R. E. Amritkar, Phys. Rev.E 70, 026101 (2004)
[7] Ma,Wang,Chen and Hu Crossover behavior of stock returns and mean square
displacements of particles governed by the Langevin equation(2013)
[8] A. Einstein, Ann. Phys. (Leipzig) 17, 549 (1905).
[9] 數學傳播第九卷第三期 漫談布朗運動-----李育嘉
[10] L. Bachelier, Ann. Sci. Ecole Norm. Sup. s`erie 3,17, 21 (1900)
[11] 財務統計 傅承德 中央研究院統計科學研究所
[12] Cowles, A. (1933). Can stock market forecasters forecast?Econometrica,309-324.
[13] Cowles, A. and John, H. E. (1937). Some a posteriori probabilities in stock market action. Econometrica, 5, 280-294
[14] Working, H. (1934). A random-difference series for use in the analysis of time series. Journal of the American Statistical Association, 29, 11-24
[15] Kendall, M. G. (1953). The analysis of economic time-series. Part 1. Prices. J ournal of the Royal Statistical Society, 96, 11-25
[16] A first course in probability / Sheldon Ross
[17] J. P. Bouchaud,M. Potters,Theory of Financial Risks second reprint
[18] 論數學遊戲 張維忠 數學傳播 30卷4期, pp. 83-94
[19] Van Den Heuvel, M., Mandl, R., & Pol, H. H. (2008). Normalized cut group clustering of resting-state FMRI data. PLoS One, 3(4), e2001.
[20] Albert-László Barabási & Réka Albert (October 1999). "Emergence of scaling in random networks". Science 286 (5439): 509–512
[21] R. C. Prim: Shortest connection networks and some generalizations. In: Bell System Technical Journal, 36 (1957), pp. 1389–1401
[22] Joseph. B. Kruskal: On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem. In: Proceedings of the American Mathematical Society, Vol 7, No. 1 (Feb, 1956), pp. 48–50
[23] Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. Introduction to Algorithms, Second Edition. MIT Press and McGraw-Hill, 2001. ISBN 0-262-03293-7. Section 23.2: The algorithms of Kruskal and Prim, pp. 567–574.
[24] R. N. Mantegna,Eur. Phys. J. B. 11, 193–197, (1999)
[25] PEDRO J. BALLESTER, W. GRAHAM RICHARDS Vol. 28, No. 10 .Journal of Computational Chemistry		zh_TW