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随机矩阵理论运用于金融领域中研究金融相关系数矩阵的相关性，相关系数矩阵是网络构建中的关键因素，本文将随机矩阵理论与网络构建相结合，研究基于随机矩阵的金融网络模型. 本文选取上海证券市场的股票数据，将其中的股票数据分成四个阶段，基于随机矩阵理论，讨论金融相关系数矩阵和随机矩阵的特征值统计性质，并在此基础上对现有的去噪方法进行改进，建立更适合构建金融网络的相关系数矩阵，并构建金融网络模型. 然后，基于随机矩阵理论和网络的关键节点分析比较去噪前后的金融网络以及噪声网络，发现对网络去噪后仍保留了原始网络的关键重要的信息，而噪声信息对应的是原始网络中度比较小的节点所代表的信息. 最后，基于去噪网络，分析金融网络的拓扑结构，如最小生成树、模体和社团结构，发现改进后的金融网络的拓扑性质更加明显，结构更加紧密.Random matrix theory is applied to study the correlation between different financial correlation coefficient matrices in the financial field. Correlation coefficient matrix is a key factor for constructing a network. In this paper we relate the random matrix theory to the network construction to study the financial networks model in terms of the random matrix. We select the stock data of Shanghai stock market, and divide them into four stages. We discuss the statistical properties of eigenvalues in financial correlation coefficient matrix and random matrix based on the random matrix theory, and improve the existing denoising method to construct the correlation coefficient matrix and to make it more suitable for building financial networks. After that we can build the financial network model. Then we analyze and compare the original financial network, the denoising financial network and the noise financial network in terms of the random matrix theory and the key node of networks. It is found that the primary important information is still in the original network, and the noise information corresponds to the information which the nodes of small degree in the original network include. Finally we analyze the topological structure of the financial networks, such as the minimum spanning tree, the motif and community structure. We also find that the topological properties of the improved financial networks are more remarkable and the topological structure is more compact.
[1] Li G H, Zhang H, Luo M K 2012 Chin. Phys. B 21 128901
[2] Zhang X D, Liu X D, Zheng Y, Liu C 2013 Chin. Phys. B 22 030509
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[4] Xu Z X, Wang Y, Si H B, Feng Z M 2011 Acta Phys. Sin. 60 040501 (in Chinese) [徐赞新, 王钺, 司洪波, 冯振明 2011 60 040501]
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[8] Conlon T, Ruskin H J, Crane M 2007 Physics A 382 565
[9] Namaki A, Jafari G R, Raei R 2011 Physics A 390 3020
[10] Rojkova V, Khali Y, Elmaghraby A, Kantardzic M 2007 IEEE Int. Symp. on Sig. Proc. and Inform. Technol. Giza, December 15-17, 2007 p647
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[13] Kumar S, Deo N 2012 Phys. Rev. E86 026101
[14] Boginski V, Butenko S, Pardalos P 2005 Comput. Stats. and Dayta Anal. 48 431
[15] Wang X F, Li X, Chen G R 2006 The. and Appl. of Comp. Net.(Beijing: Tsinghua University Press) p37 (in Chinese) [汪小帆李翔陈关荣 2006复杂网络理论及其应用(北京: 清华大学出版社)第37页]
[16] Mantegna R N 1999 Eur. Phys. J. B 11 193
[17] Shen-Orr S S, Milo R, Mangan S, Alon U 2002 Nat. Genet. 31 64
[18] Milo R, Itzkovitz S, Kashtan N, Levitt R, Shen-Orr S 2008 Science 303 1538
[19] Gulbahce N, Lehmanm S 2008 Bio. Ess. 30 934
[20] Newman M E J, Girvan M 2004 Phys. Rev. E 69 026113
[21] Han H, Liu W L, Wu L Y 2013 Acta Phys. Sin. 62 168904 (in Chinese)[韩华, 刘婉璐, 吴翎燕 2013 62 168904]
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[1] Li G H, Zhang H, Luo M K 2012 Chin. Phys. B 21 128901
[2] Zhang X D, Liu X D, Zheng Y, Liu C 2013 Chin. Phys. B 22 030509
[3] Li R, Yan P L, Chen J, Li J, Li J, Zhang K W, Zhong J X 2009 Acta Phys. Sin. 58 6703 (in Chinese) [李蓉, 颜平兰, 陈健, 李俊, 李金, 张凯旺, 钟建新 2009 58 6703]
[4] Xu Z X, Wang Y, Si H B, Feng Z M 2011 Acta Phys. Sin. 60 040501 (in Chinese) [徐赞新, 王钺, 司洪波, 冯振明 2011 60 040501]
[5] Laloux L, Cizeau P, Bouchaud J P, Potters M 1999 Phys. Rev. Lett. 83 1468
[6] Plerou V, Gopikrishnan P, Rosenow B, Amaral L A N, Guhr T, Stanley H E 2002 Phys. Rev. E 65 1
[7] Sharifi S, Crane M, Shamaie A, Ruskin H 2004 Phys. A: Stats. and Theo. Phys. 335 629
[8] Conlon T, Ruskin H J, Crane M 2007 Physics A 382 565
[9] Namaki A, Jafari G R, Raei R 2011 Physics A 390 3020
[10] Rojkova V, Khali Y, Elmaghraby A, Kantardzic M 2007 IEEE Int. Symp. on Sig. Proc. and Inform. Technol. Giza, December 15-17, 2007 p647
[11] Feher K, Whelan J, Mueller S 2011 Stats. Appl. in Gene. and Mol. Biol. 10 44
[12] Namaki A, Shirazi A H, Raei R, Jafari G R 2011 Phys. A 390 3835
[13] Kumar S, Deo N 2012 Phys. Rev. E86 026101
[14] Boginski V, Butenko S, Pardalos P 2005 Comput. Stats. and Dayta Anal. 48 431
[15] Wang X F, Li X, Chen G R 2006 The. and Appl. of Comp. Net.(Beijing: Tsinghua University Press) p37 (in Chinese) [汪小帆李翔陈关荣 2006复杂网络理论及其应用(北京: 清华大学出版社)第37页]
[16] Mantegna R N 1999 Eur. Phys. J. B 11 193
[17] Shen-Orr S S, Milo R, Mangan S, Alon U 2002 Nat. Genet. 31 64
[18] Milo R, Itzkovitz S, Kashtan N, Levitt R, Shen-Orr S 2008 Science 303 1538
[19] Gulbahce N, Lehmanm S 2008 Bio. Ess. 30 934
[20] Newman M E J, Girvan M 2004 Phys. Rev. E 69 026113
[21] Han H, Liu W L, Wu L Y 2013 Acta Phys. Sin. 62 168904 (in Chinese)[韩华, 刘婉璐, 吴翎燕 2013 62 168904]
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