Abstract
A large collection of daily time series for 60 world currencies' exchange rates is considered. The correlation matrices are calculated and the corresponding Minimal Spanning Tree (MST) graphs are constructed for each of those currencies used as reference for the remaining ones. It is shown that multiplicity of the MST graphs' nodes to a good approximation develops a power like, scale free distribution with the scaling exponent similar as for several other complex systems studied so far. Furthermore, quantitative arguments in favor of the hierarchical organization of the world currency exchange network are provided by relating the structure of the above MST graphs and their scaling exponents to those that are derived from an exactly solvable hierarchical network model. A special status of the USD during the period considered can be attributed to some departures of the MST features, when this currency (or some other tied to it) is used as reference, from characteristics typical to such a hierarchical clustering of nodes towards those that correspond to the random graphs. Even though in general the basic structure of the MST is robust with respect to changing the reference currency some trace of a systematic transition from somewhat dispersed – like the USD case – towards more compact MST topology can be observed when correlations increase.
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References
L. Laloux, P. Cizeau, J.-P. Bouchaud, M. Potter, Phys. Rev. Lett. 83, 1467 (1999)
V. Plerou, P. Gopikrishnan, B. Rosenow, L.A.N. Amaral, H.E. Stanley, Phys. Rev. Lett. 83, 1471 (1999)
J. Kwapień, S. Drożdż P. Oświęcimka, Physica A 359, 589 (2006)
Y. Aiba, N. Hatano, H. Takayasu, K. Marumo, T. Shimizu, Physica A 324, 253 (2003)
Sauder School of Business, Pacific Exchange Rate System, http://fx.sauder.ubc.ca/data.html (2006)
S. Drożdż, A.Z. Górski, J. Kwapień, Eur. Phys. J. B 58, 499 (2007)
The algorithm to construct MST graphs was for the first time published by Czech mathematician, Otakar Boruvka in 1926
J. Kruskal, Proc. Am. Math. Soc. 7, 48 (1956)
C.H. Papadimitrou, K. Steigliz, Combinatorial Optimization (Prentice-Hall, Englewood Cliffs 1982)
D.B. West, Introduction to Graph Theory (Prentice-Hall, Englewood Cliffs 1996)
R.N. Mantegna, Eur. Phys. J. B 11, 193 (1999)
J.-P. Onella, A. Chakraborti, K. Kaski, J. Kertész, Phys. A 324, 247 (2003)
G. Bonanno, G. Caldarelli, F. Lillo, R.N. Mantegna, Phys. Rev. E 68, 046130 (2003)
V.A. Marchenko, L.A. Pastur, Mat. Sb. 72, 507 (1967)
A.M. Sengupta, P.P. Mitra, Phys. Rev. E 60, 3389 (1999)
J.-P. Onella, A. Chakraborti, K. Kaski, J. Kertész, A. Kanto, Phys. Rev. E 68, 056110 (2003)
G. Bonanno, G. Caldarelli, F. Lillo, S. Miccichè, N. Vandewalle, R.N. Mantegna, Eur. Phys. J. B 38, 363 (2004)
M. McDonald, O. Suleman, S. Williams, S. Howison, N.F. Johnson, Phys. Rev. E 72, 046106 (2005)
A.Z. Górski, S. Drożdż, J. Kwapień, P. Oświęcimka, Acta Phys. Pol. B 37, 2987 (2006)
M.J. Naylor, L.C. Rose, B.J. Moyle, Physica A 382, 199 (2007)
E. Ravasz, A.-L. Barabási, Phys. Rev. E 67, 026112 (2003)
J.D. Noh, Phys. Rev. E 67 045103(R) (2003)
S. Drożdż, F. Grümmer, A.Z. Górski, F. Ruf, J. Speth, Phys. A 287, 4400 (2000)
R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002)
S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Phys. Rep. 424, 175 (2006)
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Górski, A., Drożdż, S. & Kwapień, J. Scale free effects in world currency exchange network. Eur. Phys. J. B 66, 91–96 (2008). https://doi.org/10.1140/epjb/e2008-00376-5
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DOI: https://doi.org/10.1140/epjb/e2008-00376-5