JIANG Shi-Mei1, CAI Shi-Min1, ZHOU Tao1,2,3, ZHOU Pei-Ling1
1Department of Electronic Science and Technology, University of Science and Technology of China, Hefei 2300262Department of Modern Physics, University of Science and Technology of China, Hefei 2300263Department of Physics, University of Fribourg, Chemin du Muse 3, CH-1700 Fribourg, Switzerland
1Department of Electronic Science and Technology, University of Science and Technology of China, Hefei 2300262Department of Modern Physics, University of Science and Technology of China, Hefei 2300263Department of Physics, University of Fribourg, Chemin du Muse 3, CH-1700 Fribourg, Switzerland
摘要The two-phase behaviour in financial markets actually means the bifurcation phenomenon, which represents the change of the conditional probability from an unimodal to a bimodal distribution. We investigate the bifurcation phenomenon in Hang--Seng index. It is observed that the bifurcation phenomenon in financial index is not universal, but specific under certain conditions. For Hang--Seng index and randomly generated time series, the phenomenon just emerges when the power-law exponent of absolute increment distribution is between 1 and 2 with appropriate period. Simulations on a randomly generated time series suggest the bifurcation phenomenon itself is subject to the statistics of absolute increment, thus it may not be able to reflect essential financial behaviours. However, even under the same distribution of absolute increment, the range where bifurcation phenomenon occurs is far different from real market to artificial data, which may reflect certain market information.
Abstract：The two-phase behaviour in financial markets actually means the bifurcation phenomenon, which represents the change of the conditional probability from an unimodal to a bimodal distribution. We investigate the bifurcation phenomenon in Hang--Seng index. It is observed that the bifurcation phenomenon in financial index is not universal, but specific under certain conditions. For Hang--Seng index and randomly generated time series, the phenomenon just emerges when the power-law exponent of absolute increment distribution is between 1 and 2 with appropriate period. Simulations on a randomly generated time series suggest the bifurcation phenomenon itself is subject to the statistics of absolute increment, thus it may not be able to reflect essential financial behaviours. However, even under the same distribution of absolute increment, the range where bifurcation phenomenon occurs is far different from real market to artificial data, which may reflect certain market information.
[1] Anderson P W and Pines D 1988 The economy as anEvolving Complex System (Santa Fe Institute Studies in the Scienceof Complexity Proceedings) [2] Arthur W B, Durlauf S N and Lane D A 1997 The economyAs an Evolving Complex System $\amalg$: Proceedings (Santa FeInstitute Studies in the Science of Complexity Lecture Notes) [3] Kert\'{esz J and Kondor I 1997 Econophysics: AnEmergent Science (http://newton.phy.bme.hu/$\sim$kullmann/Egyetem/konyv.html) [4] Mantegna R N and Stanley H E 1999 Introduction toEconophysics: Correlations and Complexity in Finance (Cambridge:Cambridge University Press) [5] Johnson N F, Jefferies P and Hui P M 2003 FinancialMarket Complexity (Oxford: Oxford University) [6] Challet D, Marsili M and Zhang Y C 2005 MinorityGames (Oxford: Oxford University Press) [7] Bouchaud J P and Potters M 2000 Theory of FinancialRisk (Cambridge: Cambridge University Press) [8] Mandelbrot B B 1997 Fractals and Scaling in Finance:Discontinuity, Concentration, Risk (Berlin: Springer) [9] Sornette D 2000 Critical Phenomena in NaturalScience (Berlin: Springer) [10] Wang B H and Hui P M 2001 Eur. Phys. J. B {\bf 20573 [11] Cai S M et al 2006 Chin. Phys. Lett. {\bf 23 754 [12] Cai S M et al 2006 Physica A {\bf 367 337 [13] Plerou V, Gopikrishnan P and Stanley H E 2003 Nature {\bf 421 130 [14] Zheng B, Qiu T and Ren F 2004 Phys. Rev. E {\bf 69046115 [15] Potters M et al 2003 arXiv:cond-mat/0304514 [16] Plerou V, Gopikrishnan P and Stanley H E 2005 Quantitative Finance {\bf 5 519 [17] Matia K and Yamasaki K 2005 Quantitative Finance{\bf 5 513 [18] Kolmogorov A N 1958 Dokl. Akad. Nauk SSSR {\bf 119861 [19] Sinai Y G 1959 Dokl. Akad. Nauk SSSR {\bf 124 768 [20] Clauset A et al 2007 arxiv: 0706.1062 [21] Krzesinski A E et al 2007 Int. J. Theor. Appl.Finance {\bf 10\,\,89
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