Abstract.
We investigate scaling and memory effects in return intervals between price volatilities above a certain threshold q for the Japanese stock market using daily and intraday data sets. We find that the distribution of return intervals can be approximated by a scaling function that depends only on the ratio between the return interval τ and its mean 〈τ〉. We also find memory effects such that a large (or small) return interval follows a large (or small) interval by investigating the conditional distribution and mean return interval. The results are similar to previous studies of other markets and indicate that similar statistical features appear in different financial markets. We also compare our results between the period before and after the big crash at the end of 1989. We find that scaling and memory effects of the return intervals show similar features although the statistical properties of the returns are different.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R.N. Mantegna, H.E. Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge University Press, Cambridge, 2000)
R.N. Mantegna, H.E. Stanley, Nature 376, 46 (1995)
N.F. Johnson, P. Jefferies, P.M. Hui, Financial Market Complexity (Oxford University Press, Oxford, 2003)
E. Scalas, R. Gorenflo, F. Mainardi, Physica A 314, 749 (2002)
H. Takayasu, A.H. Sato, M. Takayasu, Phys. Rev. Lett. 79, 966 (1997)
C. Tsallis, C. Anteneodo, L. Borland, R. Osorio, Physica A 324, 89 (2003)
F. Lillo, R.N. Mantegna, Phys. Rev. E 62, 6126 (2000)
T. Di Matteo, Quantitative Finance 7, 21 (2007)
B.B. Mandelbrot, J. Business 36, 394 (1963)
A. Pagan, J. Empirical Finance 3, 15 (1996)
P. Gopikrishnan, V. Plerou, L.A.N. Amaral, M. Meyer, H.E. Stanley, Phys. Rev. E 60, 5305 (1999)
Y. Liu, P. Gopikrishnan, P. Cizeau, M. Meyer, C.-K. Peng, H.E. Stanley, Phys. Rev. E 60, 1390 (1999)
X. Gabaix, P. Gopikrishnan, V. Plerou, H.E. Stanley, Nature 423, 267 (2003)
Z. Ding, C.W.J. Granger, R.F. Engle, J. Empirical Finance 1, 83 (1993)
J.K. Ord, T.H. McInish, R.A. Wood, J. Finance 40, 723 (1985)
L. Harris, J. Financ. Econ. 16, 99 (1986)
G.W. Schwert, J. Finance 44, 1115 (1989)
C.W.J. Granger, Z. Ding, J. Econometrics 73, 61 (1996)
V. Plerou, P. Gopikrishnan, X. Gabaix, L.A. Nunes Amaral, H.E. Stanley, Quant. Finance 1, 262 (2001)
V. Plerou, P. Gopikrishnan, H.E. Stanley, Phys. Rev. E 71, 046131 (2005)
J.-P. Bouchard, M. Potters, Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management (Cambridge University Press, Cambridge, 2003)
F. Black, M. Scholes, J. Polit. Econ. 81, 637 (1973)
R.F. Engle, Econometrica 50, 987 (1982)
J.C. Cox, S.A. Ross, J. Finance Econ. 3, 145 (1976)
J.Y. Campbell, A.W. Lo, A.C. MacKinlay, The Econometrics of Financial Markets (Princeton University Press, Princeton, 1997)
K. Yamasaki, L. Muchnik, S. Havlin, A. Bunde, H.E. Stanley, Proc. Natl. Acad. Sci. USA 102, 9424 (2005)
F. Wang, K. Yamasaki, S. Havlin, H.E. Stanley, Phys. Rev. E 73, 026117 (2006); F. Wang, P. Weber, K. Yamasaki, S. Havlin, H.E. Stanley, Eur. Phys. J. B 55, 123 (2007); F. Wang, K. Yamasaki, S. Havlin, H.E. Stanley, (2007)
P. Weber, F. Wang, I. Vodenska-Chitkushev, S. Havlin, H.E. Stanley, Phys. Rev. E 76, 016109 (2007)
T. Kaizoji, Physica A 343, 662 (2004)
T. Kaizoji, M. Kaizoji, Physica A 336, 563 (2004)
M.A. Stephens, J. Am. Stat. Assoc. 69, 730 (1974)
R. Engle, J. Russel, Econometrica 66, 1127 (1998)
E. Scalas, T. Kaizoji, M. Kirchler, J. Huberd, A. Tedeschi, Physica A 366, 463 (2006)
N. Sazuka, Physica A 376, 500 (2007)
A. Bunde, J.F. Eichner, J.W. Kantelhardt, S. Havlin, Phys. Rev. Lett. 94, 048701 (2005)
M.M. Dacorogna, R. Gencay, U.A. Muller, R.B. Olsen, O.V. Pictet, An Introduction to High Frequency Finance (Academic Press, London, 2001)
A. Corral, Phys. Rev. Lett. 92, 108501 (2004)
A. Bunde, J.F. Eichner, S. Havlin, J.W. Kantelhardt, Physica A 342, 308 (2004)
A. Bunde, J.F. Eichner, J.W. Kantelhardt, S. Havlin, Phys. Rev. Lett. 94, 048701 (2005)
V.N. Livina, S. Havlin, A. Bunde, Phys. Rev. Lett. 95, 208501 (2005)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jung, WS., Wang, F., Havlin, S. et al. Volatility return intervals analysis of the Japanese market. Eur. Phys. J. B 62, 113–119 (2008). https://doi.org/10.1140/epjb/e2008-00123-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2008-00123-0