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Fluctuations of stock prices and their interactions network the corresponding entities in a stock market into a complex system.How a financial crisis affects the network structure,namely,the response of the structure to a financial shock,has received special attention from different fields.The response can reveal specific features of the crisis,which may shed light on the mechanism for its occurrence and provide further helpful information of the regulation of the financial system. In the literature,there have appeared some pioneering studies on this topic.From return series of stock prices,one can calculate the cross-correlation coefficient between pairs of the entities.The cross-correlation matrix is then converted into networks according to different strategies,such as the threshold method in which an entity pair is linked only when the cross-correlation coefficient is larger than a certain value,and the planar maximally filtered graph method in which the constructed network can be embedded in a 2-dimensional surface.Some interesting findings are reported. However,there are still several essential problems to be solved.First,the previous work focused mainly on the clustering of entities and linking density of the network,while we are much more interested in the detailed changes of network structure.Second,in the planar maximally filtered graph approach,the number of links keeps constant,which means that different criterions are used in the procedures of constructing the networks before and during crisis.If we use the difference between the adjacency matrices as a measure of the structural changes,there will appear a large number of spurious changes.The real changes will be submerged in the artificial noises.The problem of artificial linkages exists also in the threshold-based method.Third,the records of stock prices form a multivariate time series,which may lead to a serious spurious estimation of correlations between the entities.Finally,the record series is limited in length.From the viewpoint of statistics,the estimated cross-correlation coefficients have usually unreasonably large values of confidence interval. In the present paper,to reconstruct a reliable entity network,we use the time delay stability (TDS) method to extract dependent relationship from stock prices.If there exists an influence transferred from node A to node B,the transfer process will spend a certain time,called time delay.The method is based on a simple fact that though the transferred signals may vary,the time delay is determined by the intrinsic properties of the nodes and their link and consequently should keep constant,called time delay stability.What is more,spanning-tree is also constructed from the cross-correlation matrix,which is jointly used with the TDS to detect reliable links between the entities.Then we calculate the defferential networks,namely,the difference between the adjacency matrices corresponding to the scenarios before and in crisis durations,to measure quantitatively the structural changes of the entities network. By using this method we consider the shocks of a total of 5 financial crises occurring in the period from 1994 to 2013.A total of 30 stocks that are used to construct the Do Jones index are considered.Interestingly,the influences of the financial crises share some features,for example in the crises the entities are tightly linked into dense clusters.At the same time,the influence of each financial crisis has its own features.For instance,the global financial crisis in 2008 led to the significant changes in the raw material related industries,in which the top three entities were the Aluminum Company of America,Exxon Mobil Corporation,and Chevron Corporation.While in the European Debt crisis in August 2011,the significantly shocked entities belong to the financial and banking industries,in which the entities Citygroup Inc.,Bank of America,and JPMorgan ChaseCoare were listed as the top three. There exist various complex systems in diverse research fields.A complex system contains generally many elements that are networked by their complicated relationships.Monitoring the dynamical process of the elements and the edges produces a multivariate time series.Hence,reconstructing the network of the variables and monitoring the evolution of the network are the preliminary step to investigate the evolutionary behaviors of complex systems.Our procedure can be extended straightforwardly to the investigation of this problem.
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Keywords:
- financial crisis /
- complex network /
- time delay stability /
- differential network
[1] Cong R G, Wei Y M, Jiao J L, Fan Y 2008 Energ. Policy 36 3544
[2] Lee W Y, Jiang C X, Indro D C 2002 J. Bank Financ. 26 2277
[3] Gao X Y, AN H Z, Fang W 2012 Acta Phys. Sin. 61 098902 (in Chinese) [高湘昀, 安海忠, 方伟2012 61 098902]
[4] Heiberger R H 2014 Physica A 393 376
[5] Kazemilari M, Djauhari M A 2015 Physica A 429 62
[6] Lacasa L, Nicosia V, Latora V 2015 Sci. Rep. 51 55008
[7] Buccheri G, Marmi S, Mantegna R N 2013 Phys. Rev. E 88 012806
[8] Vyrost T,Štefan L, Baumöh E 2015 Physica A 427 262
[9] Leonidas S J 2014 Entropy 16 4443
[10] Fenn D J, Porter M A, Williams S, Mcdonald M, Johnson N F, Jones N S 2011 Phys. Rev. E 84 1713
[11] Delpini D, Battiston S, Riccaboni M, Gabbi G, Pammolli F, Caldarelli G 2013 Sci. Rep. 3 1626
[12] 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 63 138901]
[13] Nobi A, Maeng S E, Ha G G, Lee J W 2014 Physica A 407 135
[14] Qiu T, Zheng B, Ren F, Trimper S 2006 Phys. Rev. E 73 065103
[15] Oha G, Kima H Y, Ahna S W, Kwak W 2015 Physica A 419 464
[16] Mnnix M C, Shimada T, Schöfer R, Leyvraz F, Seligman T H, Guhr T, Stanley H E 2012 Sci. Rep. 2 644
[17] Kumar S, Deo N 2012 Phys. Rev. E 86 1679
[18] Song D M, Tumminello M, Zhou W X, Mantegna R N 2011 Phys. Rev. E 84 026108
[19] Jiang X F, Chen T T, Zheng B 2014 Sci. Rep. 4 5321
[20] Yang Z L, Song Y W, Duan Z F, Wang T, Zhang J 2016 Commun. Stat.-Theor. M. 45 2332
[21] Bashan A, Bartsch R P, Kantelhardt J W, Havlin S, Ivanov P C 2012 Nat. Commun. 3 702
[22] Zhou W X 2007 An Introduction to Econophysics (Shanghai: Shanghai University of Finance and Economics press) p63(in Chinese) [周炜星2007金融物理学导论(上海: 上海财经大学出版社)第63页]
[23] Deng S G, Qiu L, Yang Y, Yang H J 2016 Physica A 441 62
[24] Eom C, Oh G, Jung W S, Jeong H, Kim S 2009 Physica A 388 900
[25] Bonanno G, Caldarelli G, Lillo F, Mantegna R N 2002 Phys. Rev. E 68 352
[26] Huang J P 2013 Econophysics (Beijing: Higher Education Press) p30(in Chinese) [黄吉平2013经济物理学(北京: 高等教育出版社)第30页]
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[1] Cong R G, Wei Y M, Jiao J L, Fan Y 2008 Energ. Policy 36 3544
[2] Lee W Y, Jiang C X, Indro D C 2002 J. Bank Financ. 26 2277
[3] Gao X Y, AN H Z, Fang W 2012 Acta Phys. Sin. 61 098902 (in Chinese) [高湘昀, 安海忠, 方伟2012 61 098902]
[4] Heiberger R H 2014 Physica A 393 376
[5] Kazemilari M, Djauhari M A 2015 Physica A 429 62
[6] Lacasa L, Nicosia V, Latora V 2015 Sci. Rep. 51 55008
[7] Buccheri G, Marmi S, Mantegna R N 2013 Phys. Rev. E 88 012806
[8] Vyrost T,Štefan L, Baumöh E 2015 Physica A 427 262
[9] Leonidas S J 2014 Entropy 16 4443
[10] Fenn D J, Porter M A, Williams S, Mcdonald M, Johnson N F, Jones N S 2011 Phys. Rev. E 84 1713
[11] Delpini D, Battiston S, Riccaboni M, Gabbi G, Pammolli F, Caldarelli G 2013 Sci. Rep. 3 1626
[12] 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 63 138901]
[13] Nobi A, Maeng S E, Ha G G, Lee J W 2014 Physica A 407 135
[14] Qiu T, Zheng B, Ren F, Trimper S 2006 Phys. Rev. E 73 065103
[15] Oha G, Kima H Y, Ahna S W, Kwak W 2015 Physica A 419 464
[16] Mnnix M C, Shimada T, Schöfer R, Leyvraz F, Seligman T H, Guhr T, Stanley H E 2012 Sci. Rep. 2 644
[17] Kumar S, Deo N 2012 Phys. Rev. E 86 1679
[18] Song D M, Tumminello M, Zhou W X, Mantegna R N 2011 Phys. Rev. E 84 026108
[19] Jiang X F, Chen T T, Zheng B 2014 Sci. Rep. 4 5321
[20] Yang Z L, Song Y W, Duan Z F, Wang T, Zhang J 2016 Commun. Stat.-Theor. M. 45 2332
[21] Bashan A, Bartsch R P, Kantelhardt J W, Havlin S, Ivanov P C 2012 Nat. Commun. 3 702
[22] Zhou W X 2007 An Introduction to Econophysics (Shanghai: Shanghai University of Finance and Economics press) p63(in Chinese) [周炜星2007金融物理学导论(上海: 上海财经大学出版社)第63页]
[23] Deng S G, Qiu L, Yang Y, Yang H J 2016 Physica A 441 62
[24] Eom C, Oh G, Jung W S, Jeong H, Kim S 2009 Physica A 388 900
[25] Bonanno G, Caldarelli G, Lillo F, Mantegna R N 2002 Phys. Rev. E 68 352
[26] Huang J P 2013 Econophysics (Beijing: Higher Education Press) p30(in Chinese) [黄吉平2013经济物理学(北京: 高等教育出版社)第30页]
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