Dynamics of cluster structure in financial correlation matrix. (English) Zbl 1380.91142
Summary: The correlation dimensions in the financial market are calculated and used as a measure to study the cluster structure in the correlation coefficient matrix. First, based on the existing model, we present a toy model. Using the model-generated data, we find that the clearer cluster structure corresponds to a smaller dimension. It implies that the correlation dimension can be used as a measure of the cluster structure in the correlation coefficient matrix. Finally, we use the algorithm to compute the clusters in the real market and verify the previous empirical evidence. The results show that the cluster structure in the financial correlation coefficient matrix may change with time. The correlation dimension is smaller after the financial crisis, indicating that the cluster structure is clearer after the financial crisis.
MSC:
| 91G70 | Statistical methods; risk measures |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
Keywords:
correlation dimension; cluster algorithm; financial network; financial crisis; correlation coefficient matrixSoftware:
DowdReferences:
| [1] | chung Fu, T., A review on time series data mining, Eng Appl Artif Intell, 24, 1, 164-181 (2011) |
| [2] | Liao, T., Clustering of time series data-a survey, Pattern Recognit, 38, 11, 1857-1874 (2005) · Zbl 1077.68803 |
| [3] | Grassberger, P.; Procaccia, I., The theory of chaotic attractors, 170-189 (2004), Springer New York |
| [4] | Grassberger, P.; Procaccia, I., Characterization of strange attractors, Phys Rev Lett, 50, 5, 346 (1983) |
| [5] | Grassberger, P., Generalized dimensions of strange attractors, Phys Lett A, 97, 6, 227-230 (1983) |
| [6] | Beck, C.; Schlögl, F., Thermodynamics of chaotic systems: an introduction, 116 (1995), Cambridge University Press · Zbl 0847.58051 |
| [7] | Mayfield, E.; Mizrach, B., On determining the dimension of real-time stock price data, J Bus Econ Stat, 10, 3, 367-374 (1992) |
| [8] | S. Soofi, A.; Galka, A., Measuring the complexity of currency markets by fractal dimension analysis, Int J Theor Appl Finance, 6, 06, 553-563 (2003) · Zbl 1079.91061 |
| [9] | Wang, H.; Chen, G.; Lü, J., Complex dynamical behaviors of daily data series in stock exchange, Phys Lett A, 333, 3, 246-255 (2004) · Zbl 1123.91359 |
| [10] | Camastra, F.; Vinciarelli, A., Estimating the intrinsic dimension of data with a fractal-based method, IEEE Trans Pattern Anal Mach Intell, 24, 10, 1404-1407 (2002) |
| [11] | Kégl, B., Intrinsic dimension estimation using packing numbers, Adv Neural Inf Process Syst, 681-688 (2002) |
| [12] | Huang, W.-Q.; Zhuang, X.-T.; Yao, S., A network analysis of the chinese stock market, Physica A, 388, 2956-2964 (2009) |
| [13] | Tse, C. K.; Liu, J.; Lau, F. C., A network perspective of the stock market, J Empirical Finance, 17, 659-667 (2010) |
| [14] | Nobi, A.; Maeng, S. E.; Ha, G. G.; Lee, J. W., Effects of global financial crisis on network structure in a local stock market, Physica A, 407, 135-143 (2014) |
| [15] | Nobi, A.; Lee, S.; Kim, D. H.; Lee, J. W., Correlation and network topologies in global and local stock indices, Phys Lett A, 378, 2482-2489 (2014) |
| [16] | Onnela, J.-P.; Chakraborti, A.; Kaski, K., Asset trees and asset graphs in financial markets, Phys Scr, T106, 48-54 (2003) · Zbl 1129.91323 |
| [17] | Kim, K.; Kim, S. Y.; Ha, D.-H., Characteristics of networks in financial markets, Comput Phys Commun, 177, 184-185 (2007) · Zbl 1196.91045 |
| [18] | Boginski, V.; Butenko, S.; M. Pardalos, P., Mining market data : a network approach, Comput Oper Res, 33, 3171-3184 (2006) · Zbl 1113.90079 |
| [19] | Namaki, A.; Shirazi, A. H.; Raei, R.; Jafari, G. R., Network analysis of a financial market based on genuine correlation and threshold method, Physica A, 390, 3835-3841 (2011) |
| [20] | Boginski, V.; Butenko, S.; M. Pardalos, P., Statistical analysis of financial networks, Comput Stat Data Anal, 48, 431-443 (2005) · Zbl 1429.62460 |
| [21] | Nie, C.-X., Correlation dimension of financial market, Physica A, 473, 632-639 (2017) |
| [22] | Mantegna, R. N., Hierarchical structure in financial markets, Eur Phys J B, 11, 193-197 (1999) |
| [23] | Nanda, S. R.; Mahanty, B.; Tiwari, M. K., Clustering indian stock market data for portfolio management, Expert Syst Appl, 37, 8793-9798 (2010) |
| [24] | Musmeci, N.; Aste, T.; Matteo, T., Relation between financial market structure and the real economy: comparison between clustering methods, PLoS ONE, e0116201 (2015) |
| [25] | Tola, V.; Lillo, F.; Gallegati, M.; Mantegna, R. N., Cluster analysis for portfolio optimization, J Econ Dyn Control, 32, 235-258 (2008) · Zbl 1181.91303 |
| [26] | Dose, C.; Cincotti, S., Clustering of financial time series with application to index and enhanced index tracking portfolio, Physica A, 355, 145-151 (2005) |
| [27] | Pattarin, F.; Paterlini, S.; Minerva, T., Clustering financial time series: an application to mutual funds style analysis, Comput Stat Data Anal, 47, 353-372 (2004) · Zbl 1429.62476 |
| [28] | D’Urso, P.; Cappelli, C.; Lallo, D. D.; Massari, R., Clustering of financial time series, Physica A, 392, 2114-2129 (2013) |
| [29] | Focardi, S. M.; Fabozzi, F. J., A methodology for index tracking based on timeseries clustering, Quant Finance, 4, 417-425 (2004) · Zbl 1405.91552 |
| [30] | Y. Campbell, J.; W. Lo, A.; MacKinlay, A., The econometrics of financial markets, 219-252 (1997), Princeton University Press · Zbl 0927.62113 |
| [31] | Bun, J.; Bouchaud, J.-P.; Potters, M., Cleaning large correlation matrices: tools from random matrix theory, Phys Rep, 666, 1-109 (2017) · Zbl 1359.15031 |
| [32] | Lillo, F.; Mantegna, R. N., Spectral density of the correlation matrix of factor models: a random matrix theory approach, Phys Rev E, 72, 016219 (2005) |
| [33] | N. Ferreira, L.; Zhao, L., Time series clustering via community detection in networks, Inf Sci, 326, 227-242 (2016) · Zbl 1390.68526 |
| [34] | Fortunato, S., Community detection in graphs, Phys Rep, 486, 3, 75-174 (2010) |
| [35] | D. Malliaros, F.; Vazirgiannis, M., Clustering and community detection in directed networks:a survey, Phys Rep, 533, 4, 95-142 (2013) · Zbl 1356.05151 |
| [36] | Schaeffer, S. E., Graph clustering, Comput Sci Rev, 1, 1, 27-64 (2007) · Zbl 1302.68237 |
| [37] | Newman, M. E.J., Fast algorithm for detecting community structure in networks, Phys Rev E, 69, 066133 (2004) |
| [38] | Dowd, K., Measuring market risk (2005), John Wiley & Sons, Ltd |
| [39] | Clauset, A.; Newman, M. E.J.; Moore, C., Finding community structure in very large networks, Phys Rev E, 70, 066111 (2004) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
