On superstatistical multiplicative-noise processes

Queirós, Sı́lvio M. Duarte

doi:10.1590/s0103-97332008000200001

Cited by 22 publications

(12 citation statements)

References 34 publications

(28 reference statements)

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“…The bias factor q is called the entropic index and q ∈ ℜ. Recently, it has been proposed that q is connected to the dynamics of the system [3,4,5,6,7,8]. Besides representing a generalization, the nonextensive entropy S q , as much as S BG , is positive, concave and Lesche-stable (∀q > 0).…”

Section: Introductionmentioning

confidence: 99%

Finite-size analysis of a two-dimensional Ising model within a nonextensive approach

Crokidakis¹,

Soares-Pinto²,

Reis³

et al. 2009

Phys. Rev. E

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In this work we present a thorough analysis of the phase transitions that occur in a ferromagnetic 2D Ising model, with only nearest-neighbors interactions, in the framework of the Tsallis nonextensive statistics. We performed Monte Carlo simulations on square lattices with linear sizes L ranging from 32 up to 512. The statistical weight of the Metropolis algorithm was changed according to the nonextensive statistics. Discontinuities in the m(T) curve are observed for q ≤ 0.5. However, we have verified only one peak on the energy histograms at the critical temperatures, indicating the occurrence of continuous phase transitions. For the 0.5 < q ≤ 1.0 regime, we have found continuous phase transitions between the ordered and the disordered phases, and determined the critical exponents via finite-size scaling. We verified that the critical exponents α, β and γ depend on the entropic index q in the range 0.5 < q ≤ 1.0 in the form α(q) = (10 q 2 − 33 q + 23)/20, β(q) = (2 q − 1)/8 and γ(q) = (q 2 − q + 7)/4. On the other hand, the critical exponent ν does not depend on q. This suggests a violation of the scaling relations 2 β + γ = d ν and α + 2 β + γ = 2 and a nonuniversality of the critical exponents along the ferro-paramagnetic frontier.

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Section: Introductionmentioning

confidence: 99%

Finite-size analysis of a two-dimensional Ising model within a nonextensive approach

Crokidakis¹,

Soares-Pinto²,

Reis³

et al. 2009

Phys. Rev. E

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“…Indeed, they provide a plausible mathematical basis for the ubiquity of distributions such as the q-Gaussians (generically q-exponentials) as actually observed in many natural, artificial, and even social systems (see Chapter 7). A variety of physical situations and interesting questions related with nonlinear Fokker-Planck equations are discussed in [192][193][194][195][196].…”

Section: 3) Which Provide Interesting Hintsmentioning

confidence: 99%

Introduction to Nonextensive Statistical Mechanics

Tsallis¹

2009

278

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“…From the analysis of high-frequency data, it was found the trading volume distribution, p(v), is actually compatible with asymptotic power-law distributions, namely the F-distribution [13][14][15][16][17][18][19]. In respect of the autocorrelation function, although prior analyses had pointed to a power-law decay as well [20], subsequent results indicated that quantity is best described by a composition of exponential regimes [21], a result which upheld a "superstatistical" [22] approach to p(v) (for a recent review on trading volume please consult [23]). Combining those results, it is possible to attribute those statistical features to the nonstationarity of the trading activity-defined as the number of active agents in the market-on which the (local) average trading volume depends.…”

Section: Introductionmentioning

confidence: 99%

Intraday Seasonalities and Nonstationarity of Trading Volume in Financial Markets: Individual and Cross-Sectional Features

Graczyk

Queirós²

2016

PLoS ONE

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We study the intraday behaviour of the statistical moments of the trading volume of the blue chip equities that composed the Dow Jones Industrial Average index between 2003 and 2014. By splitting that time interval into semesters, we provide a quantitative account of the nonstationary nature of the intraday statistical properties as well. Explicitly, we prove the well-known ∪-shape exhibited by the average trading volume—as well as the volatility of the price fluctuations—experienced a significant change from 2008 (the year of the “subprime” financial crisis) onwards. That has resulted in a faster relaxation after the market opening and relates to a consistent decrease in the convexity of the average trading volume intraday profile. Simultaneously, the last part of the session has become steeper as well, a modification that is likely to have been triggered by the new short-selling rules that were introduced in 2007 by the Securities and Exchange Commission. The combination of both results reveals that the ∪ has been turning into a ⊔. Additionally, the analysis of higher-order cumulants—namely the skewness and the kurtosis—shows that the morning and the afternoon parts of the trading session are each clearly associated with different statistical features and hence dynamical rules. Concretely, we claim that the large initial trading volume is due to wayward stocks whereas the large volume during the last part of the session hinges on a cohesive increase of the trading volume. That dissimilarity between the two parts of the trading session is stressed in periods of higher uproar in the market.

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On superstatistical multiplicative-noise processes

Cited by 22 publications

References 34 publications

Finite-size analysis of a two-dimensional Ising model within a nonextensive approach

Finite-size analysis of a two-dimensional Ising model within a nonextensive approach

Introduction to Nonextensive Statistical Mechanics

Intraday Seasonalities and Nonstationarity of Trading Volume in Financial Markets: Individual and Cross-Sectional Features

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