Abstract
We apply random matrix theory (RMT) to investigate the structure of cross-correlation in 20 global financial time series after the global financial crisis of 2008. We find that the largest eigenvalue deviates from the RMT prediction and is sensitive to the financial crisis. We find that the components of eigenvectors corresponding to the second largest eigenvalue changes sign in response to the crisis. We show that 20 global financial indices exhibit multifractality. We find that the origin of multifractality is due to the long-range correlations as well as broad probability function in the financial indices, with the exception of the index of Taiwan, as in all other indices the multifractal degree for shuffled and surrogate series is weaker than the original series. We fit the binomial multifractal model to the global financial indices.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
T Guhr, A Muller-Groeling and H A Weidenmuller, Phys. Rep. 299, 189 (1998)
M L Mehta, Random matrices (Academic Press, Boston, 1991)
M J Bowick and E Brézin, Phys. Lett. B 268, 21 (1991) J Feinberg and A Zee, J. Stat. Phys. 87, 473 (1997)
R N Mantegna and H E Stanley, An introduction to econophysics (Cambridge University Press, Cambridge, UK, 2000) J-P Bouchaud and M Potters, Theory of financial risks (Cambridge University Press, Cambridge, UK, 2000)
A M Sengupta and P P Mitra, Phys. Rev. E 60, 3389 (1999)
J P Bouchaud, A Matacz and M Potters, Phys. Rev. Lett. 87, 228701 (2001)
Y Liu, P Gopikrishnan, P Cizeau, M Meyer, C K Peng and H E Stanley, Phys. Rev. E 60, 1390 (1999)
R N Mantegna and H E Stanley, Nature 376, 46 (1995)
L Laloux, P Cizeau, J P Bouchaud and M Potters, Phys. Rev. Lett. 83, 1467 (1999)
V Plerou, P Gopikrishnan, B Rosenow, L A Nunes Amaral and H E Stanley, Phys. Rev. Lett. 83, 1471 (1999)
V Plerou, P Gopikrishnan, L A Nunes Amaral, M Meyer and H E Stanley, Phys. Rev. E 60, 6519 (1999)
X Gobaix, P Gopikrishnan, V Plerou and H E Stanley, Nature 423, 267 (2003)
P Gopikrishnan, B Rosenow, V Plerou and H E Stanley, Phys. Rev. E 64, 035106 (2001)
V Kulkarni and N Deo, Eur. Phys. J. B 60, 101 (2007)
R K Pan and S Sinha, Phys. Rev. E 76, 046116 (2007)
M Marsili and Y C Zhang, Phys. Rev. Lett. 80, 2741 (1998)
J Shen and B Zheng, Europhys. Lett. 86, 48005 (2009)
D Wang, B Podobnik, D Horvatić and H E Stanley, Phys. Rev. E 83, 046121 (2011)
I Meric, S Kim, J H Kim and G Meric, J. Money, Investment Banking 3, 47 (2008)
L S Junior and I D Paula Franca, Physica A 391, 187 (2012)
T Conlon, H J Ruskin and M Crane, Physica A 388, 705 (2009)
S Kumar and N Deo, Phys. Rev. E 86, 026101 (2012)
J W Kantelhardt, S A Zschiegner, E Koscielny-Bunde, S Havlin, A Bunde and H E Stanley, Physica A 316, 87 (2002)
C-K Peng, S V Buldyrev, S Havlin, M Simons, H E Stanley and A L Goldberger, Phys. Rev. E 49, 1685 (1994) S M Ossadnik, S B Buldyrev, A L Goldberger, S Havlin, R N Mantegna, C-K Peng, M Simon and H E Stanley, Biophys. J. 67, 64 (1994)
J W Kantelhardt, E Koscielny-Bunde, H H A Rego, S Havlin and A Bunde, Physica A 295, 441 (2001) K Hu, P Ch Ivanov, Z Chen, P Carpena and H E Stanley, Phys. Rev. E 64, 011114 (2001)
P Ch Ivanov, L A N Amaral, A L Goldberger, S Havlin, M G Rosenblum, Z Struzik and H E Stanley, Nature 399, 461 (1999)
H E Stanley and P Meakin, Nature 335, 505 (1998)
S Kumar and N Deo, Physica A 388, 1593 (2009)
C Borghesi, M Marsili and S Micciche, Phys. Rev. E 76, 026104 (2007)
P Oświȩcimka, J Kwapiań and S DroŻdŻ, Physica A 347, 626 (2005)
W-X Zhou, Europhys. Lett. 88, 28004 (2009)
L Zunino et al, Physica A 387, 6558 (2008)
L Zunino et al, Chaos, Solitons and Fractals 41, 2331 (2009)
J Tenenbaum, D Horvatić, S C Bajić, B Pehlivanović, B Podobnik and H E Stanley, Phys. Rev. E 82, 046104 (2010)
B Podobnik, D Wang, D Horvatic, I Grosse and H E Stanley, Europhys. Lett. 90, 68001 (2010)
S Kumar and N Deo, Econophysics of systemic risks and network dynamics (Springer-Verlag, Italia, 2013) pp. 261–275
T Schreiber and A Schmitz, Phys. Rev. Lett. 77, 635 (1996)
J Theiler, S Eubank, A Longtin, B Galdrikian and J D Farmer, Physica D 58, 77 (1992)
J Feder, Fractals (Plenum Press, New York, 1988)
A-L Barabási and T Vicsek, Phys. Rev. A 44, 2730 (1991)
Acknowledgements
The authors would like to thank Prof. Sanjay Jain for encouragement and discussions.
They also acknowledge the University Faculty R &D Grant for financial support.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
KUMAR, S., DEO, N. Analysing correlations after the financial crisis of 2008 and multifractality in global financial time series. Pramana - J Phys 84, 317–325 (2015). https://doi.org/10.1007/s12043-015-0935-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12043-015-0935-6