Economics and Finance: q-Statistical Stylized Features Galore

Tsallis, Constantino

doi:10.3390/e19090457

Cited by 35 publications

(35 citation statements)

References 121 publications

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“…It should be emphasized that this q stat value is fully consistent with the bounds obtained from several independent studies involving the nonextensive framework (see, e.g. [14]). Fig.…”

Section: Stationary Q = Q Statsupporting

confidence: 90%

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Nonextensive triplets in stock market indices

Stošić

2019

Physica A: Statistical Mechanics and its Applications

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Stock market indices are one of the most investigated complex systems in econophysics.Here we extend the existing literature on stock markets in connection with nonextensive statistical mechanics. We explore the nonextensivity of price volatilities for 34 major stock market indices between 2010 and 2019. We discover that stock markets follow nonextensive statistics regarding equilibrium, relaxation and sensitivity. We find nonextensive behavior in stock markets for developed countries, but not for developing countries. Distances between nonextensive triplets suggest that some stock markets might share similar nonextensive dynamics, while others are widely different. The current findings strongly indicate that the stock market represents a system whose physics is properly described by nonextensive statistical mechanics. Our results shed light on the complex nature of stock market indices, and establish another formal link with the nonextensive theory.

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“…It should be emphasized that this q stat value is fully consistent with the bounds obtained from several independent studies involving the nonextensive framework (see, e.g. [14]). Fig.…”

Section: Stationary Q = Q Statsupporting

confidence: 90%

“…For a classical BG process such correlation should decay in exponential fashion, but volatilities in stock markets are known to exhibit long-range correlations [14]. Fig.…”

Section: Relaxation Q = Q Relmentioning

confidence: 99%

Nonextensive triplets in stock market indices

Stošić

2019

Physica A: Statistical Mechanics and its Applications

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“…They are also of utmost interest to physicists as these models exhibit different complex dynamical and statistical phenomena, reminiscent of the complex phenomena, such as phase transitions [10,11], dissipative structures [12,13] or non-extensive thermodynamics [14,15], common in statistical physics. This interest is well grounded in the empirical data too, as complex statistical and dynamical patterns are observed in the empirical data from socio-economic systems as well [8,16,17]. While there is a well established set of stylized facts for the financial markets, e.g., [18], numerous empirical studies in opinion dynamics have not yet helped to establish even a basic set of stylized facts, which could be seen as a goal for the theoretical models.…”

Section: Introductionmentioning

confidence: 99%

Modeling of the Parties' Vote Share Distributions

Kononovičius

2018

Acta Phys. Pol. A

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Competition between varying ideas, people and institutions fuels the dynamics of socio-economic systems. Numerous analyses of the empirical data extracted from different financial markets have established a consistent set of stylized facts describing statistical signatures of the competition in the financial markets. Having an established and consistent set of stylized facts helps to set clear goals for theoretical models to achieve. Despite similar abundance of empirical analyses in sociophysics, there is no consistent set of stylized facts describing the opinion dynamics. In this contribution we consider the parties' vote share distributions observed during the Lithuanian parliamentary elections. We show that most of the time empirical vote share distributions could be well fitted by numerous different distributions. While discussing this peculiarity we provide arguments, including a simple agent-based model, on why the beta distribution could be the best choice to fit the parties' vote share distributions. arXiv:1709.07655v2 [physics.soc-ph]

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“…To assess the use of the ESJS as a goodness-of-fit measure, we provide experimental results with simulated and empirical data with respect to various parametric distributions including the Normal, Uniform, Log-normal, Gamma, Weibull, Beta, Exponential, Pareto [3] and q-Gaussian [37,38] distributions. It is worth to note that q-Gaussian distribution is equivalent to Student's t-distribution [3].…”

Section: Experiments and Analysismentioning

confidence: 99%

Empirical survival Jensen-Shannon divergence as a goodness-of-Fit measure for maximum likelihood estimation and curve fitting

Levene

Kononovičius

2019

Communications in Statistics - Simulation and Computation

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The coefficient of determination, known as R 2 , is commonly used as a goodness-of-fit criterion for fitting linear models. R 2 is somewhat controversial when fitting nonlinear models, although it may be generalised on a case-by-case basis to deal with specific models such as the logistic model. Assume we are fitting a parametric distribution to a data set using, say, the maximum likelihood estimation method. A general approach to measure the goodness-of-fit of the fitted parameters, which is advocated herein, is to use a nonparametric measure for comparison between the empirical distribution, comprising the raw data, and the fitted model. In particular, for this purpose we put forward the Survival Jensen-Shannon divergence (SJS) and its empirical counterpart (ESJS) as a metric which is bounded, and is a natural generalisation of the Jensen-Shannon divergence. We demonstrate, via a straightforward procedure making use of the ESJS, that it can be used as part of maximum likelihood estimation or curve fitting as a measure of goodness-of-fit, including the construction of a confidence interval for the fitted parametric distribution. Furthermore, we show the validity of the proposed method with simulated data, and three empirical data sets.for nonlinear models, [5], where the author recommends to define R 2 as a comparison of a given model to the null model, claiming that this view allows for the generalisation of R 2 . Further, in [6] the inappropriateness of R 2 for nonlinear models is clearly demonstrated via a series of Monte Carlo simulations. In [7], a novel R 2 measure based on the Kullback-Leibler divergence [8] was proposed as a measure of goodness-of-fit for regression models in the exponential family. In addition, in [9] problems with using R 2 for assessing goodnessof-fit in linear mixed models with random effects were highlighted, and in [10] an improved extension was proposed in the context of both linear and generalised linear mixed models. Despite numerous proposals to address the issues with R 2 for nonlinear models, many of them are ad-hoc, and, as noted in [11], should be applied with caution. In summary, there seems to be a lack of general purpose goodness-of-fit measures that could be applied to nonlinear models, which is the main issue we attempt to redress with the ESJS.Alternative nonparametric methods have also been proposed. In particular, the Akaike information criterion (AIC) and its counterpart the Bayesian information criterion (BIC) [12,13], are widely used estimators for model selection. Both AIC and BIC are asymptotically valid maximum likelihood estimators, with penalty terms to discourage overfitting. We stress that goodness-of-fit measures how well a single model fits the observed data, while model selection compares the predictive accuracy of two models relative to each other [12,14]. The likelihood ratio test is also an established method for model selection between a null model and an alternative maximum likelihood model [15,16]. Despite the popularity of maximum likelihood meth...

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Economics and Finance: q-Statistical Stylized Features Galore

Cited by 35 publications

References 121 publications

Nonextensive triplets in stock market indices

Nonextensive triplets in stock market indices

Modeling of the Parties' Vote Share Distributions

Empirical survival Jensen-Shannon divergence as a goodness-of-Fit measure for maximum likelihood estimation and curve fitting

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