Statistical Properties of the Foreign Exchange Network at Different Time Scales: Evidence from Detrended Cross-Correlation Coefficient and Minimum Spanning Tree

Entropy - Tập 15 Số 5 - Trang 1643-1662
Gang‐Jin Wang1, Chi Xie2,1, Yijun Chen1, Shou Chen2,1
1College of Business Administration, Hunan University, Changsha 410082, China
2Center of Finance and Investment Management, Hunan University, Changsha 410082, China

Tóm tắt

We investigate the statistical properties of the foreign exchange (FX) network at different time scales by two approaches, namely the methods of detrended cross-correlation coefficient (DCCA coefficient) and minimum spanning tree (MST). The daily FX rates of 44 major currencies in the period of 2007–2012 are chosen as the empirical data. Based on the analysis of statistical properties of cross-correlation coefficients, we find that the cross-correlation coefficients of the FX market are fat-tailed. By examining three MSTs at three special time scales (i.e., the minimum, medium, and maximum scales), we come to some conclusions: USD and EUR are confirmed as the predominant world currencies; the Middle East cluster is very stable while the Asian cluster and the Latin America cluster are not stable in the MSTs; the Commonwealth cluster is also found in the MSTs. By studying four evaluation criteria, we find that the MSTs of the FX market present diverse topological and statistical properties at different time scales. The scale-free behavior is observed in the FX network at most of time scales. We also find that most of links in the FX network survive from one time scale to the next.

Từ khóa


Tài liệu tham khảo

Mantegna, R.N., and Stanley, H.E. (2000). An Introduction to Econophysics: Correlations and Complexity in Finance, Cambridge University Press.

2012, Physical approach to complex systems, Phys. Rep., 515, 115, 10.1016/j.physrep.2012.01.007

Wang, 2012, Cross-correlations between WTI crude oil market and US stock market: A perspective from econophysics, Acta Phys. Pol. B, 43, 2021, 10.5506/APhysPolB.43.2021

Wang, 2013, Cross-correlations between Renminbi and four major currencies in the Renminbi currency basket, Physica A, 392, 1418, 10.1016/j.physa.2012.11.035

Kenett, D.Y., Raddant, M., Lux, T., and Ben-Jacob, E. (2012). Evolvement of uniformity and volatility in the stressed global financial village. PLoS One, 7.

Siqueira, 2010, Correlations and cross-correlations in the Brazilian agrarian commodities and stocks, Physica A, 389, 2739, 10.1016/j.physa.2010.01.040

Wang, G.J., and Xie, C. (2013). Cross-correlations between the CSI 300 spot and futures markets. Nonlinear Dyn.

Kenett, 2010, Dynamics of stock market correlations, Czech AUCO Econ. Rev., 4, 330

Kenett, D.Y., Preis, T., Gur-Gershgoren, G., and Ben-Jacob, E. (2012). Quantifying meta-correlations in financial markets. Europhys. Lett., 99.

Mantegna, 1999, Hierarchical structure in financial markets, Eur. Phys. J. B, 11, 193, 10.1007/s100510050929

Tumminello, 2005, A tool for filtering information in complex systems, Proc. Natl. Acad. Sci. USA, 102, 10421, 10.1073/pnas.0500298102

Boginski, 2005, Statistical analysis of financial networks, Comput. Stat. Data Anal., 48, 431, 10.1016/j.csda.2004.02.004

Huang, 2009, A network analysis of the Chinese stock market, Physica A, 388, 2956, 10.1016/j.physa.2009.03.028

Onnela, 2004, Clustering and information in correlation based financial networks, Eur. Phys. J. B, 38, 353, 10.1140/epjb/e2004-00128-7

Franca, 2012, Correlation of financial markets in times of crisis, Physica A, 391, 187, 10.1016/j.physa.2011.07.023

Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L.A.N., Guhr, T., and Stanley, H.E. (2002). Random matrix approach to cross correlations in financial data. Phys. Rev. E, 65.

Laloux, 1999, Noise dressing of financial correlation matrices, Phys. Rev. Lett., 83, 1467, 10.1103/PhysRevLett.83.1467

Plerou, 1999, Universal and nonuniversal properties of cross correlations in financial time series, Phys. Rev. Lett., 83, 1471, 10.1103/PhysRevLett.83.1471

Podobnik, B., Wang, D., Horvatic, D., Grosse, I., and Stanley, H.E. (2010). Time-lag cross-correlations in collective phenomena. Europhys. Lett., 90.

Podobnik, B., and Stanley, H.E. (2008). Detrended cross-correlation analysis: A new method for analyzing two nonstationary time series. Phys. Rev. Lett., 100.

Zhou, W.X. (2008). Multifractal detrended cross-correlation analysis for two nonstationary signals. Phys. Rev. E, 77.

Horvatic, D., Stanley, H.E., and Podobnik, B. (2011). Detrended cross-correlation analysis for non-stationary time series with periodic trends. Europhys. Lett., 94.

Wang, 2012, Similarity measure and topology evolution of foreign exchange markets using dynamic time warping method: Evidence from minimal spanning tree, Physica A, 391, 4136, 10.1016/j.physa.2012.03.036

Onnela, 2002, Dynamic asset trees and portfolio analysis, Eur. Phys. J. B, 30, 285, 10.1140/epjb/e2002-00380-9

Onnela, J.P., Chakraborti, A., Kaski, K., Kertesz, J., and Kanto, A. (2003). Dynamics of market correlations: Taxonomy and portfolio analysis. Phys. Rev. E, 68.

Jiang, 2010, Complex stock trading network among investors, Physica A, 389, 4929, 10.1016/j.physa.2010.07.024

Tabak, 2010, Topological properties of stock market networks: The case of Brazil, Physica A, 389, 3240, 10.1016/j.physa.2010.04.002

Tumminello, 2010, Correlation, hierarchies, and networks in financial markets, J. Econ. Behav. Organ., 75, 40, 10.1016/j.jebo.2010.01.004

Aste, T., Shaw, W., and di Matteo, T. (2010). Correlation structure and dynamics in volatile markets. New J. Phys., 12.

Pozzi, 2010, The use of dynamical networks to detect the hierarchical organization of financial market sectors, Eur. Phys. J. B, 73, 3, 10.1140/epjb/e2009-00286-0

Gao, Y.C., Wei, Z.W., and Wang, B.H. (2013). Dynamic evolution of financial network and its relation to economic crises. Int. J. Mod. Phys. C, 24.

Yang, C., Shen, Y., and Xia, B. (2013). Evolution of Shanghai stock market based on maximal spanning trees. Mod. Phys. Lett. B, 27.

Kenett, D.Y., Tumminello, M., Madi, A., Gur-Gershgoren, G., Mantegna, R.N., and Ben-Jacob, E. (2010). Dominating clasp of the financial sector revealed by partial correlation analysis of the stock market. PLoS One, 5.

Kenett, D.Y., Preis, T., Gur-Gershgoren, G., and Ben-Jacob, E. (2012). Dependency network and node influence: Application to the study of financial markets. Int. J. Bifurcat. Chaos., 22.

Sieczka, 2009, Correlations in commodity markets, Physica A, 388, 1621, 10.1016/j.physa.2009.01.004

McDonald, M., Suleman, O., Williams, S., Howison, S., and Johnson, N.F. (2005). Detecting a currency’s dominance or dependence using foreign exchange network trees. Phys. Rev. E, 72.

Mizuno, 2006, Correlation networks among currencies, Physica A, 364, 336, 10.1016/j.physa.2005.08.079

Naylor, 2007, Topology of foreign exchange markets using hierarchical structure methods, Physica A, 382, 199, 10.1016/j.physa.2007.02.019

Gworek, 2009, Structure and evolution of the foreign exchange networks, Acta Phys. Pol. B, 40, 175

Gworek, 2009, Analysis of a network structure of the foreign currency exchange market, J. Econ. Interact. Coord., 4, 55, 10.1007/s11403-009-0047-9

Gworek, 2010, Sign and amplitude representation of the forex networks, Acta Phys. Pol. A, 117, 681, 10.12693/APhysPolA.117.681

Keskin, 2011, Topology of the correlation networks among major currencies using hierarchical structure methods, Physica A, 390, 719, 10.1016/j.physa.2010.10.041

Jang, 2011, Currency crises and the evolution of foreign exchange market: Evidence from minimum spanning tree, Physica A, 390, 707, 10.1016/j.physa.2010.10.028

2008, Scale free effects in world currency exchange network, Eur. Phys. J. B, 66, 91, 10.1140/epjb/e2008-00376-5

Gu, 2013, Is the efficiency of stock market correlated with multifractality? An evidence from the Shanghai stock market, Physica A, 392, 361, 10.1016/j.physa.2012.09.008

Mantegna, 1995, Scaling behaviour in the dynamics of an economic index, Nature, 376, 46, 10.1038/376046a0

Drożdż, S., Kwapień, J., Oświȩcimka, P., and Rafał, R. (2010). The foreign exchange market: Return distributions, multifractality, anomalous multifractality and the Epps effect. New J. Phys., 12.

Zebende, 2011, DCCA cross-correlation coefficient: Quantifying level of cross-correlation, Physica A, 390, 614, 10.1016/j.physa.2010.10.022

Peng, 1994, Mosaic organization of DNA nucleotides, Phys. Rev. E, 49, 1685, 10.1103/PhysRevE.49.1685

Vassoler, 2012, DCCA cross-correlation coefficient apply in time series of air temperature and air relative humidity, Physica A, 391, 2438, 10.1016/j.physa.2011.12.015

Zebende, 2013, DCCA cross-correlation coefficient differentiation: Theoretical and practical approaches, Physica A, 392, 1756, 10.1016/j.physa.2013.01.011

Cao, 2012, Multifractal detrended cross-correlations between the Chinese exchange market and stock market, Physica A, 391, 4855, 10.1016/j.physa.2012.05.035

Podobnik, B., Jiang, Z.Q., Zhou, W.X., and Stanley, H.E. (2011). Statistical tests for power-law cross-correlated processes. Phys. Rev. E, 84.

Wang, G.J., Xie, C., Chen, S., Yang, J.J., and Yang, M.Y. (2013). Random matrix theory analysis of cross-correlations in the U.S. stock market: Evidence from Pearson correlation coefficient and detrended cross-correlation coefficient. Physica A.

Pacific Exchange Rate Service. Available online: http://fx.sauder.ubc.ca/data.html.

Wang, 2010, Cross-correlations between Chinese A-share and B-share markets, Physica A, 389, 5468, 10.1016/j.physa.2010.08.029

Kantelhardt, 2002, Multifractal detrended fluctuation analysis of nonstationary time series, Physica A, 316, 87, 10.1016/S0378-4371(02)01383-3

Kruskal, 1956, On the shortest spanning subtree of a graph and the traveling salesman problem, Proc. Am. Math. Soc., 7, 48, 10.1090/S0002-9939-1956-0078686-7

Djauhari, 2013, Minimal spanning tree problem in stock networks analysis: An efficient algorithm, Physica A, 392, 2226, 10.1016/j.physa.2012.12.032

Vandewalle, 2001, Non-random topology of stock markets, Quant. Econom., 1, 372

Clauset, 2009, Power-law distributions in empirical data, SIAM Rev., 51, 661, 10.1137/070710111