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复杂网络能够解决许多金融问题，能够发现金融市场的拓扑结构特征，反映不同金融主体之间的相互依赖关系.相关性度量在金融复杂网络构建中至关重要.通过将多元金融时间序列符号化，借鉴文本特征提取以及信息论的方法，定义了一种基于文本互信息的相关系数.为检验方法的有效性，分别构建了基于不同相关系数（Pearson和文本互信息）和不同网络缩减方法（阈值和最小生成树）的4个金融复杂网络模型.在阈值网络中提出了使用分位数来确定阈值的方法，将相关系数6等分，取第4部分的中点作为阈值，此时基于Pearson和文本互信息的阈值模型将会有相近的边数，有利于这两种模型的对比.数据使用了沪深两地证券市场地区指数收盘价，时间从2006年1月4日至2016年12月30日，共计2673个交易日.从网络节点相关性看，基于文本互信息的方法能够体现出大约20%的非线性相关关系；在网络整体拓扑指标上，本文计算了4种指标，结果显示能够使所保留的节点联系更为紧密，有效提高保留节点的重要性以及挖掘出更好的社区结构；最后，计算了阈值网络的动态指标，将数据按年分别构建网络，缩减方法只用了阈值方法，结果显示本文提出的方法在小世界动态和网络度中心性等指标上能够成功捕捉到样本区间内存在的两次异常波动.此外，本文构建的地区金融网络具有服从幂律分布、动态稳定性、一些经济欠发达地区在金融地区网络中占据重要地位等特性.Complex networks are widely used in many problems of the financial field. It can be used to find the topological structure properties of the financial markets and to embody the interdependence between different financial entities. The correlation is important to create the complex networks of the financial markets. A novel approach to incorporating textual mutual information into financial complex networks as a measure of the correlation coefficient is developed in the paper. We will symbolize the multivariate financial time series firstly, and then calculate correlation coefficient with textual mutual information. Finally, we will convert it into a distance. To test the proposed method, four complex network models will be built with different correlation coefficients (Pearson's and textual mutual information's) and different network simplification methods (the threshold and minimum spanning tree). In addition, for the threshold networks, a quantile method is proposed to estimate the threshold automatically. The correlation coefficients are divided into 6 equal parts. And the midpoint of the 4th interval will be taken as the threshold according to our experience, which can make the MI methods and Pearson methods have the closest number of edges to compare the two methods. The data come from the closing prices of Chinese regional indexes including both Shanghai and Shenzhen stock market. The data range from January 4, 2006 to December 30, 2016, including 2673 trading days. In view of node correlation, the numerical results show that there are about 20% of the nonlinear relationships of the Chinese regional financial complex networks. In view of the network topology, four topological indicators for the regional financial complex network models will be calculated in the paper. For average weighted degree, the novel method can make the reserved nodes closely compared with Pearson's correlation coefficient. For network betweenness centralization, it can improve the betweenness importance of reserved nodes effectively. From the perspective of modularity, the novel method can detect better community structures. Finally, in dynamic network topology features, the data of regional indexes will be equally divided yearly for constructing complex network separately. The simplification method used in the section is the threshold method. The numerical results show that the proposed methods can successfully capture the two-abnormal fluctuation in the sample interval with the dynamics of the small-world and the network degree centralization. In addition, we find that the proposed regional financial network models follow the power-law distribution and are dynamically stable. Some developing regions are more important than the developed ones in the regional financial networks.
[1] Mantegna R N, Stanley H E 1995 Nature 376 46
[2] Tang Z P, Chen W H, Ran M 2017 Acta Phys. Sin. 66 120203 (in Chinese) [唐振鹏, 陈尾虹,冉梦 2017 物理学报 66 120203]
[3] Huang J P 2015 Phys. Rep. 564 1
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[6] Fama E F 1970 J. Finance 25 383
[7] Haldane A G, May R M 2011 Nature 469 351
[8] Han H, Wu L Y, Song N N 2014 Acta Phys. Sin. 63 138901 (in Chinese) [韩华, 吴翎燕, 宋宁宁 2014 物理学报 63 138901]
[9] Mantegna R N 1999 Eur. Phys. J. B 11 193
[10] Huang W Q, Zhuang X T, Yao S 2009 Physica A 388 2956
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[12] Wiliński M, Sienkiewicz A, Gubiec T, Kutner R, Struzik Z R 2013 Physica A 392 5963
[13] Fiedor P 2015 Acta Phys. Pol. A 127 A33
[14] Wang G J, Xie C, Stanley H E 2018 Comput. Econ. 51 607
[15] Fiedor P, Holda A 2016 J. Risk Finance 17 93
[16] Jang W, Lee J, Chang W 2011 Physica A 390 707
[17] Sousa A M Y R, Takayasu H, Takayasu M 2014 Proceedings of the International Conference on Social Modeling and Simulation, plus Econophysics Colloquium 2014 Kobe, Japan, Nov. 4-6, 2014 p3
[18] Fan H 2014 Acta Phys. Sin. 63 038902 (in Chinese) [范宏 2014 物理学报 63 038902]
[19] De Masi G, Fujiwara Y, Gallegati M, Greenwald B, Stiglitz J E 2011 Evolut. Inst. Econ. Rev. 7 209
[20] Gao X Y, An H Z, Liu H H, Ding Y H 2011 Acta Phys. Sin. 60 068902 (in Chinese) [高湘昀, 安海忠,刘红红, 丁颖辉 2011 物理学报 60 068902]
[21] Zhong W, An H, Fang W, Gao X, Dong D 2016 Appl. Energy 165 868
[22] Meng H, Xie W J, Jiang Z Q, Podobnik B, Zhou W X, Stanley H E 2014 Sci. Rep. 4 3655
[23] Meng H, Xie W J, Zhou W X 2015 Int. J. Mod. Phys. B 29 1550181
[24] Wang G J, Xie C 2015 Physica A 424 176
[25] Lee J, Youn J, Chang W 2012 Physica A 391 1354
[26] Tumminello M, Di Matteo T, Aste T, Mantegna R N 2007 Eur. Phys. J. B 55 209
[27] Mnnix M C, Schãfer R, Guhr T 2010 Physica A 389 4828
[28] Yang C, Shen Y, Xia B 2012 Mod. Phys. Lett. B 27 1350022
[29] Nobia A, Maenga S E, Haa G G, Lee J W 2014 Physica A 407 135
[30] Fiedor P 2015 Acta Phys. Pol. A 127 863
[31] Sandoval Junior L, Franca I D P 2012 Physica A 391 187
[32] Qiu L, Jia T M, Yang H J 2016 Acta Phys. Sin. 65 198901 (in Chinese) [邱路, 贾天明, 杨会杰 2016 物理学报 65 198901]
[33] Fiedor P 2014 Phys. Rev. E: Stat. Nonlinear Soft Matter Phys. 89 052801
[34] Shannon C E 1948 AT. T. Tech. J. 27 379
[35] You T, Fiedor P, Hołda A 2015 J. Risk Financial Manag. 8 266
[36] Fiedor P 2014 Proceedings of the 2014 IEEE Conference on Computational Intelligence for Financial Engineering London, United Kingdom, Mar. 27-28, 2014 p247
[37] Vergara J R, Estévez P A 2014 Neural Comput. Appl. 24 175
[38] Coletti P 2016 Physica A 463 246
[39] Brida J G, Gómez D M, Risso W A 2009 Expert Syst. Appl. 36 7721
[40] Brida J G, Risso W A 2010 Expert Syst. Appl. 37 3846
[41] Nooy W D, Mrvar A, Batagelj V 2011 Exploratory Social Network Analysis with Pajek 2ED (New York: Cambridge University Press) pp344-348
[42] Blondel V D, Guillaume J L, Lambiotte R, Lefebvre E 2008 J. Stat. Mech. 2008 P10008
[43] Heiberger R H 2014 Physica A 393 376
[44] Clauset A, Shalizi C, Newman M 2009 SIAM Rev. 51 661
[45] Xu R, Wong W K, Chen G, Huang S 2017 Sci. Rep. 7 41379
[46] Snijders T A B, van de Bunt G G, Steglich C E G 2010 Soc. Networks 32 44
[47] Qiu T, Zheng B, Chen G 2010 New J. Phys. 12 043057
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[1] Mantegna R N, Stanley H E 1995 Nature 376 46
[2] Tang Z P, Chen W H, Ran M 2017 Acta Phys. Sin. 66 120203 (in Chinese) [唐振鹏, 陈尾虹,冉梦 2017 物理学报 66 120203]
[3] Huang J P 2015 Phys. Rep. 564 1
[4] Chen T T, Zheng B, Li Y, Jiang X F 2017 Front. Phys. 12 128905
[5] Bodie Z, Kane A, Marcus A J 2012 Essentials of Investments 9ED (New York: McGraw-Hill Education) pp217-222, 235-242
[6] Fama E F 1970 J. Finance 25 383
[7] Haldane A G, May R M 2011 Nature 469 351
[8] Han H, Wu L Y, Song N N 2014 Acta Phys. Sin. 63 138901 (in Chinese) [韩华, 吴翎燕, 宋宁宁 2014 物理学报 63 138901]
[9] Mantegna R N 1999 Eur. Phys. J. B 11 193
[10] Huang W Q, Zhuang X T, Yao S 2009 Physica A 388 2956
[11] Namaki A, Shirazi A H, Raei R, Jafari G R 2011 Physica A 390 3835
[12] Wiliński M, Sienkiewicz A, Gubiec T, Kutner R, Struzik Z R 2013 Physica A 392 5963
[13] Fiedor P 2015 Acta Phys. Pol. A 127 A33
[14] Wang G J, Xie C, Stanley H E 2018 Comput. Econ. 51 607
[15] Fiedor P, Holda A 2016 J. Risk Finance 17 93
[16] Jang W, Lee J, Chang W 2011 Physica A 390 707
[17] Sousa A M Y R, Takayasu H, Takayasu M 2014 Proceedings of the International Conference on Social Modeling and Simulation, plus Econophysics Colloquium 2014 Kobe, Japan, Nov. 4-6, 2014 p3
[18] Fan H 2014 Acta Phys. Sin. 63 038902 (in Chinese) [范宏 2014 物理学报 63 038902]
[19] De Masi G, Fujiwara Y, Gallegati M, Greenwald B, Stiglitz J E 2011 Evolut. Inst. Econ. Rev. 7 209
[20] Gao X Y, An H Z, Liu H H, Ding Y H 2011 Acta Phys. Sin. 60 068902 (in Chinese) [高湘昀, 安海忠,刘红红, 丁颖辉 2011 物理学报 60 068902]
[21] Zhong W, An H, Fang W, Gao X, Dong D 2016 Appl. Energy 165 868
[22] Meng H, Xie W J, Jiang Z Q, Podobnik B, Zhou W X, Stanley H E 2014 Sci. Rep. 4 3655
[23] Meng H, Xie W J, Zhou W X 2015 Int. J. Mod. Phys. B 29 1550181
[24] Wang G J, Xie C 2015 Physica A 424 176
[25] Lee J, Youn J, Chang W 2012 Physica A 391 1354
[26] Tumminello M, Di Matteo T, Aste T, Mantegna R N 2007 Eur. Phys. J. B 55 209
[27] Mnnix M C, Schãfer R, Guhr T 2010 Physica A 389 4828
[28] Yang C, Shen Y, Xia B 2012 Mod. Phys. Lett. B 27 1350022
[29] Nobia A, Maenga S E, Haa G G, Lee J W 2014 Physica A 407 135
[30] Fiedor P 2015 Acta Phys. Pol. A 127 863
[31] Sandoval Junior L, Franca I D P 2012 Physica A 391 187
[32] Qiu L, Jia T M, Yang H J 2016 Acta Phys. Sin. 65 198901 (in Chinese) [邱路, 贾天明, 杨会杰 2016 物理学报 65 198901]
[33] Fiedor P 2014 Phys. Rev. E: Stat. Nonlinear Soft Matter Phys. 89 052801
[34] Shannon C E 1948 AT. T. Tech. J. 27 379
[35] You T, Fiedor P, Hołda A 2015 J. Risk Financial Manag. 8 266
[36] Fiedor P 2014 Proceedings of the 2014 IEEE Conference on Computational Intelligence for Financial Engineering London, United Kingdom, Mar. 27-28, 2014 p247
[37] Vergara J R, Estévez P A 2014 Neural Comput. Appl. 24 175
[38] Coletti P 2016 Physica A 463 246
[39] Brida J G, Gómez D M, Risso W A 2009 Expert Syst. Appl. 36 7721
[40] Brida J G, Risso W A 2010 Expert Syst. Appl. 37 3846
[41] Nooy W D, Mrvar A, Batagelj V 2011 Exploratory Social Network Analysis with Pajek 2ED (New York: Cambridge University Press) pp344-348
[42] Blondel V D, Guillaume J L, Lambiotte R, Lefebvre E 2008 J. Stat. Mech. 2008 P10008
[43] Heiberger R H 2014 Physica A 393 376
[44] Clauset A, Shalizi C, Newman M 2009 SIAM Rev. 51 661
[45] Xu R, Wong W K, Chen G, Huang S 2017 Sci. Rep. 7 41379
[46] Snijders T A B, van de Bunt G G, Steglich C E G 2010 Soc. Networks 32 44
[47] Qiu T, Zheng B, Chen G 2010 New J. Phys. 12 043057
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