Abstract.
In this article we study the dependence degree of the traded volume of the Dow Jones 30 constituent equities by using a nonextensive generalised form of the Kullback-Leibler information measure. Our results show a slow decay of the dependence degree as a function of the lag. This feature is compatible with the existence of non-linearities in this type time series. In addition, we introduce a dynamical mechanism whose associated stationary probability density function (PDF) presents a good agreement with the empirical results.
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References
Nonextensive Entropy - Interdisciplinary Applications, edited by M. Gell-Mann, C. Tsallis (Oxford Univiversity Press, New York, 2004)
R.N. Mantegna, H.E. Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge University Press, 1999); J.-P. Bouchaud, M. Potters, Theory of Financial Risks: From Statistical Physics to Risk Management (Cambridge University Press, 2000); J. Voit, The Statistical Mechanics of Financial Markets (Springer-Verlag, Berlin, 2003)
P. Gopikrishnan, V. Plerou, X. Gabaix, H.E. Stanley, Phys. Rev. E 62, R4493 (2000)
R. Osorio, L. Borland, C. Tsallis, in reference gm-ct, p. 321
S.M. Duarte Queirós, Europhys. Lett. 73, 339 (2005)
S.M. Duarte Queirós, Quantit. Finance 5, 475 (2005)
T. Bollerslev, J. Econometrics 31, 307 (1986); S.J. Taylor, Modelling Financial Time Series (Wiley, New York, 1986); S.M. Duarte Queirós, C. Tsallis, Eur. Phys. J. B 48, 139 (2005)
C. Tsallis, J. Stat. Phys. 52, 479 (1988). Bibliography: http://tsallis.cat.cbpf.br/biblio.htm
C. Tsallis, Phys. Rev. E 58, 1442 (1998); L. Borland, A.R. Plastino, C. Tsallis, J. Math. Phys. 39, 6490 (1998); L. Borland, A.R. Plastino, C. Tsallis, J. Math. Phys. 40, 2196 (1998)
S. Kullback, R.A. Leibler, Ann. Math. Stat. 22, 79 (1961)
H. Risken, The Fokker-Planck Equation: Methods of Solution and Applications, 2nd edition (Springer-Verlag, Berlin, 1989)
As a matter of fact it can be shown that: \(x^a e_q^{- \frac{x}{b}} = \Bigl[\frac{b}{q-1} \Bigr]^{\frac{1}{q-1}} x^{a - \frac{1}{q-1}}\, e_q^{-\frac{b / (q-1)^2}{x}}\;\;\;\;(q>1)\). In other words, by a simple redefinition of parameters the inverted q-Gamma can be written as the q-Gamma PDF
W. Feller, Ann. of Math. 54, 173 (1951)
L.G. Moyano, J. de Souza, S.M. Duarte Queirós, e-print arXiv:physics/0512240 (preprint, 2005)
S.M. Duarte Queirós, C. Tsallis, in progress
C. Beck, E.G.D. Cohen, Physica A 322, 267 (2003)
C. Beck, E.G.D. Cohen, H.L. Swinney, Phys. Rev. E 72, 056133 (2005)
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de Souza, J., Moyano, L. & Duarte Queirós, S. On statistical properties of traded volume in financial markets. Eur. Phys. J. B 50, 165–168 (2006). https://doi.org/10.1140/epjb/e2006-00130-1
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DOI: https://doi.org/10.1140/epjb/e2006-00130-1