Analyzing the stock market based on the structure of kNN network

Abstract This paper systematically studies the structure of the financial kNN (k-nearest neighbor) network. First, we use the eigenvalues and eigenvectors of the financial correlation matrix to analyze the structure of the network. We find that the degree is related to the average correlation coefficient, and furthermore, it also has a relationship between the components of the eigenvector corresponding to the maximum eigenvalue. We apply existing research to confirm that the community structure of the kNN network can be used to cluster financial time series. Finally, empirical studies based on financial markets in three countries show that there is a high correlation between the community structure and dimensions. Therefore, this study shows that the structure of the financial kNN network is related to the properties of the correlation matrix, and it extracts a meaningful correlation structure.

[1]  H. Stanley,et al.  Community Analysis of Global Financial Markets , 2016 .

[2]  Chun-Xiao Nie,et al.  Constructing financial network based on PMFG and threshold method , 2018 .

[3]  Sai-Ping Li,et al.  Rényi indices of financial minimum spanning trees , 2016 .

[4]  Francesco Masulli,et al.  A survey of kernel and spectral methods for clustering , 2008, Pattern Recognit..

[5]  Wen-Jie Xie,et al.  Club Convergence of House Prices: Evidence from China's Ten Key Cities , 2015, 1503.05550.

[6]  Kousuke Yakubo,et al.  Multifractality of complex networks. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Yong Hu,et al.  A new information dimension of complex networks , 2013, ArXiv.

[8]  Zu-Guo Yu,et al.  Determination of multifractal dimensions of complex networks by means of the sandbox algorithm. , 2014, Chaos.

[9]  T. Aste,et al.  The use of dynamical networks to detect the hierarchical organization of financial market sectors , 2010 .

[10]  Cai Xu,et al.  The Fractal Dimensions of Complex Networks , 2009 .

[11]  Yue Yang,et al.  Complex network-based time series analysis , 2008 .

[12]  Panos M. Pardalos,et al.  Statistical analysis of financial networks , 2005, Comput. Stat. Data Anal..

[13]  L. da F. Costa,et al.  Characterization of complex networks: A survey of measurements , 2005, cond-mat/0505185.

[14]  Anil K. Jain.  Data clustering: 50 years beyond K-means , 2010, Pattern Recognit. Lett..

[15]  Tak-Chung Fu,et al.  A review on time series data mining , 2011, Eng. Appl. Artif. Intell..

[16]  Panos M. Pardalos,et al.  Mining market data: A network approach , 2006, Comput. Oper. Res..

[17]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[18]  S. Havlin,et al.  Self-similarity of complex networks , 2005, Nature.

[19]  Satu Elisa Schaeffer,et al.  Graph Clustering , 2017, Encyclopedia of Machine Learning and Data Mining.

[20]  Elizabeth Ann Maharaj,et al.  Cluster of Time Series , 2000, J. Classif..

[21]  B. Zheng,et al.  Structure of local interactions in complex financial dynamics , 2014, Scientific Reports.

[22]  Donald B. Johnson,et al.  Efficient Algorithms for Shortest Paths in Sparse Networks , 1977, J. ACM.

[23]  Lucas Lacasa,et al.  Correlation dimension of complex networks , 2012, Physical review letters.

[24]  Michalis Vazirgiannis,et al.  Clustering and Community Detection in Directed Networks: A Survey , 2013, ArXiv.

[25]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[26]  O. Shanker,et al.  DEFINING DIMENSION OF A COMPLEX NETWORK , 2007 .

[27]  Resul Eryigit,et al.  Network structure of cross-correlations among the world market indices , 2009 .

[28]  Francis C. M. Lau,et al.  A network perspective of the stock market , 2010 .

[29]  Seong Eun Maeng,et al.  Effects of global financial crisis on network structure in a local stock market , 2014 .

[30]  Chun-xiao Nie,et al.  Relationship between Entropy and Dimension of Financial Correlation-Based Network , 2018, Entropy.

[31]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

[32]  Leonidas Sandoval Junior.  Cluster formation and evolution in networks of financial market indices , 2011, Algorithmic Finance.

[33]  Deock-Ho Ha,et al.  Characteristics of networks in financial markets , 2007, Comput. Phys. Commun..

[34]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[35]  M Tumminello,et al.  A tool for filtering information in complex systems. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[36]  M E J Newman,et al.  Fast algorithm for detecting community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  E. Ben-Jacob,et al.  Dominating Clasp of the Financial Sector Revealed by Partial Correlation Analysis of the Stock Market , 2010, PloS one.

[38]  Zhi-Qiang Jiang,et al.  Correlation structure and principal components in the global crude oil market , 2014, 1405.5000.

[39]  Jae Woo Lee,et al.  Correlation and network topologies in global and local stock indices , 2014 .

[40]  Camellia Sarkar,et al.  Unveiling the multi-fractal structure of complex networks , 2016, 1610.06662.

[41]  Sankaran Mahadevan,et al.  Tsallis information dimension of complex networks , 2014, ArXiv.

[42]  Wei Li,et al.  Structure and dynamics of stock market in times of crisis , 2016 .

[43]  R. Mantegna.  Hierarchical structure in financial markets , 1998, cond-mat/9802256.

[44]  Xiong Xiong,et al.  Market correlation structure changes around the Great Crash , 2016 .

[45]  Rosario N. Mantegna,et al.  Evolution of Correlation Structure of Industrial Indices of US Equity Markets , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[46]  Rui Xu,et al.  Survey of clustering algorithms , 2005, IEEE Transactions on Neural Networks.

[47]  Sankaran Mahadevan,et al.  Box-covering algorithm for fractal dimension of weighted networks , 2013, Scientific Reports.

[48]  William T. Shaw,et al.  Correlation structure and dynamics in volatile markets , 2010 .

[49]  V. Plerou,et al.  Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series , 1999, cond-mat/9902283.

[50]  Pasi Fränti,et al.  Fast Agglomerative Clustering Using a k-Nearest Neighbor Graph , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[51]  Xintian Zhuang,et al.  A network analysis of the Chinese stock market , 2009 .

[52]  T. Aste,et al.  Correlation based networks of equity returns sampled at different time horizons , 2007 .

[53]  M. Newman,et al.  Finding community structure in very large networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  Steven J. Leon.  Linear Algebra With Applications , 1980 .

[55]  Liang Zhao,et al.  Time series clustering via community detection in networks , 2015, Inf. Sci..

[56]  Daijun Wei,et al.  A generalized volume dimension of complex networks , 2014 .

[57]  T. Warren Liao,et al.  Clustering of time series data - a survey , 2005, Pattern Recognit..

[58]  Boris Podobnik,et al.  Systemic risk and spatiotemporal dynamics of the US housing market , 2013, Scientific Reports.

[59]  Zu-Guo Yu,et al.  Multifractal analysis of complex networks , 2011, 1108.5014.

[60]  O. Shanker,et al.  Graph zeta function and dimension of complex network , 2007 .

[61]  Pasi Fränti,et al.  Outlier Detection Using k-Nearest Neighbour Graph , 2004, ICPR.

[62]  Santo Fortunato,et al.  Community detection in graphs , 2009, ArXiv.

[63]  K. Kaski,et al.  Asset Trees and Asset Graphs in Financial Markets , 2003 .

[64]  J. Bouchaud,et al.  Noise Dressing of Financial Correlation Matrices , 1998, cond-mat/9810255.

[65]  A. H. Shirazi,et al.  Network analysis of a financial market based on genuine correlation and threshold method , 2011 .

[66]  Rosario N. Mantegna,et al.  Evolution of Worldwide Stock Markets, Correlation Structure and Correlation Based Graphs , 2011 .

[67]  D. Sornette,et al.  Exploring self-similarity of complex cellular networks: The edge-covering method with simulated annealing and log-periodic sampling , 2006, cond-mat/0605676.