Non-extensive properties, multifractality, and inefficiency degree of the Athens Stock Exchange General Index

Stavroyiannis, Stavros; Makris, Ilias A.; Nikolaidis, Vasilis N.

doi:10.1016/j.irfa.2009.11.005

Cited by 20 publications

(6 citation statements)

References 53 publications

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“…As we have shown the experimental results of this study indicate clearly the non-Gaussian Tsallis q-Gaussian character of the probability distributions of the S & P 500 and TVIX time series. This result is in contrast with the mainstream hypothesis that economic dynamics can be studied through the Newtonian approach which treats the economic fluctuations as linear perturbations near the equilibrium, while the dynamics follow random walks and the statistics are Gaussian, independent and identically distributed (Chian A.C.-L. et al, 2006;Stavroyiannis et al, 2010). Moreover, Tsallis q-triplet analysis showed that the Tsallis non-extensive q-statistics have been verified both for the S & P 500 and TVIX time series indicating nonextensivity as well as the multi-fractal and multi-scale dynamics of the stock market underlying dynamics.…”

Section: Discussionmentioning

confidence: 61%

Tsallis q - triplet and Stock Market Indices : The cases of S & P 500 and TVIX

Iliopoulos¹,

Pavlos²,

Magafas³

et al. 2015

JESTR

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In this study we present results of the evaluation of q − triplet of Tsallis non-extensive statistics concerning two time stock market time series, Standart & Poor's 500 (S & P) 500 and TVIX. The analysis of the results, support the hypothesis in which economic dynamics from physical point of view correspond to far from equilibrium spatial distributed non-linear dynamics. In particular, the analysis of the stock market time series revealed underlying complex dynamics, indicating clearly that the statistics of the dynamics in the multifractal phase space can be described by Tsallis distribution functions of power law and heavy tails forms. The non-extensive character of the underlying dynamics is related to the existence of long range interactions in space and time, as well as the interaction in many scales. In addition, the detailed analysis of S & P index unraveled the existence of non-equilibrium phase transitions depicted clearly in the variations of Tsallis q-triplet values. These phase transitions are connected with non-equilibrium stationary states of economical dynamics derived from processes of strong self organization which correspond to local maxima of Tsallis entropy, while the changes in the control parameters can induce new phase transitions and shifts to new metaequilibrium steady states of maximizing Tsallis entropy. These phase transitions lead to changes in Tsallis qtriplet values which correspond to multi-fractal changes in the formation of the phase state and an alteration in the phenomenology of the economical system. Finally, these characteristics also indicate the existence of fractional dynamics in the phase space which can be described through fractional Fokker-Planck equations and anomalous diffusion equations. The solutions of these equations are fractional spatiotemporal functions and non-Gaussian distributions functions which fall into the category of Levy distributions and Tsallis distributions.

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Section: Discussionmentioning

confidence: 61%

Tsallis q - triplet and Stock Market Indices : The cases of S & P 500 and TVIX

Iliopoulos¹,

Pavlos²,

Magafas³

et al. 2015

JESTR

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“…But as the values of the Hurst exponent in this case are not significantly far from 0.5, they might have a hint of randomness and this certainly adds to the uncertainty in the forecasting of the present three stock market indices. Study also reveals that both SENSEX and NSE data are multifractal in nature [8][9][10][11][12][13][14][15][16][17][18][19][20]. These two observations point out the possibility of multi-periodic or/and pseudo-periodic behaviour of the SEN-SEX and NIFTY indices.…”

Section: Introductionmentioning

confidence: 89%

Search for the periodicity of the prime Indian and American stock exchange indices using date-compensated discrete Fourier transform

Samadder¹,

Ghosh

Basu

2015

Chaos, Solitons & Fractals

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“…The merit of this approach is that the average correction of scale changes is incorporated without requiring deflators or discounting factors, but in contrast to other choices, a nonlinear transformation is used (Stavroyiannis, Makris, & Nikolaidis, 2010). The time series under consideration are the major historical indices up to 31-Dec-2010 that is, DJIA from Oct-1-1928 consisting of 20655 observations, NASDAQ from Feb-5-1971 consisting of 10067 observations, S&P500 from Jan-3-1950 consisting of 15384 observations, FTSE100 from Apr-2-1984 consisting of 6758 observations, CAC from Mar-1-1990 consisting of 5268 observations, and DAX from Nov-26-1990 consisting of 5079 observations therefore, examining several extended financial time series of varying magnitude and including different historical crashes.…”

Section: The Datamentioning

confidence: 99%