scholarly journals Equity Market Description under High and Low Volatility Regimes Using Maximum Entropy Pairwise Distribution

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1307
Author(s):  
Mauricio A. Valle ◽  
Jaime F. Lavín ◽  
Nicolás S. Magner
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Principle ◽  
Ferromagnetic State ◽  
Second Order ◽  
Distribution Model ◽  
Subprime Crisis ◽  
Second Moments ◽  
Entropy Principle ◽  
Volatility Regimes ◽  
Equity Indices

The financial market is a complex system in which the assets influence each other, causing, among other factors, price interactions and co-movement of returns. Using the Maximum Entropy Principle approach, we analyze the interactions between a selected set of stock assets and equity indices under different high and low return volatility episodes at the 2008 Subprime Crisis and the 2020 Covid-19 outbreak. We carry out an inference process to identify the interactions, in which we implement the a pairwise Ising distribution model describing the first and second moments of the distribution of the discretized returns of each asset. Our results indicate that second-order interactions explain more than 80% of the entropy in the system during the Subprime Crisis and slightly higher than 50% during the Covid-19 outbreak independently of the period of high or low volatility analyzed. The evidence shows that during these periods, slight changes in the second-order interactions are enough to induce large changes in assets correlations but the proportion of positive and negative interactions remains virtually unchanged. Although some interactions change signs, the proportion of these changes are the same period to period, which keeps the system in a ferromagnetic state. These results are similar even when analyzing triadic structures in the signed network of couplings.

scholarly journals An Integrative Dynamic Model of Colombian Population Distribution, Based on the Maximum Entropy Principle and Matter, Energy, and Information Flow

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1172
Author(s):  
César Cardona-Almeida ◽  
Nelson Obregón ◽  
Fausto A. Canales
Keyword(s):  
Maximum Entropy ◽  
Information Exchange ◽  
New Technologies ◽  
Population Distribution ◽  
Knowledge Society ◽  
Maximum Entropy Principle ◽  
Distribution Model ◽  
Human Society ◽  
Natural Systems ◽  
Entropy Principle

Human society has increased its capacity to exploit natural resources thanks to new technologies, which are one of the results of information exchange in the knowledge society. Many approaches to understanding the interactions between human society and natural systems have been developed in the last decades, and some have included considerations about information. However, none of them has considered information as an active variable or flowing entity in the human–natural/social-ecological system, or, moreover, even as a driving force of their interactions. This paper explores these interactions in socio-ecological systems by briefly introducing a conceptual frame focused on the exchange of information, matter, and energy. The human population is presented as a convergence variable of these three physical entities, and a population distribution model for Colombia is developed based on the maximum entropy principle to integrate the balances of related variables as macro-state restrictions. The selected variables were electrical consumption, water demand, and higher education rates (energy, matter, and information). The final model includes statistical moments for previous population distributions. It is shown how population distribution can be predicted yearly by combining these variables, allowing future dynamics exploration. The implications of this model can contribute to bridging information sciences and sustainability studies.

On Singular Closures for the 5-Moment System in Kinetic Gas Theory

2015 ◽  
Vol 17 (2) ◽  
pp. 371-400 ◽  
Author(s):  
Roman Pascal Schaerer ◽  
Manuel Torrilhon
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Principle ◽  
Second Order ◽  
Gas Flows ◽  
Moment Equations ◽  
Moment System ◽  
Entropy Principle ◽  
Kinetic Gas Theory ◽  
Closure Theory ◽  
Non Equilibrium

AbstractMoment equations provide a flexible framework for the approximation of the Boltzmann equation in kinetic gas theory. While moments up to second order are sufficient for the description of equilibrium processes, the inclusion of higher order moments, such as the heat flux vector, extends the validity of the Euler equations to non-equilibrium gas flows in a natural way.Unfortunately, the classical closure theory proposed by Grad leads to moment equations, which suffer not only from a restricted hyperbolicity region but are also affected by non-physical sub-shocks in the continuous shock-structure problem if the shock velocity exceeds a critical value. Amore recently suggested closure theory based on the maximum entropy principle yields symmetric hyperbolic moment equations. However, if moments higher than second order are included, the computational demand of this closure can be overwhelming. Additionally, it was shown for the 5-moment system that the closing flux becomes singular on a subset of moments including the equilibrium state.Motivated by recent promising results of closed-form, singular closures based on the maximum entropy approach, we study regularized singular closures that become singular on a subset of moments when the regularizing terms are removed. In order to study some implications of singular closures, we use a recently proposed explicit closure for the 5-moment equations. We show that this closure theory results in a hyperbolic system that can mitigate the problem of sub-shocks independent of the shock wave velocity and handle strongly non-equilibrium gas flows.

Weibull Model Based on the Maximum Entropy Principle and its Applications on Elements Grade Distribution

2012 ◽  
Vol 204-208 ◽  
pp. 4851-4854 ◽  
Author(s):  
Li Wan ◽  
Peng Chen ◽  
Xu Yi Hu
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Principle ◽  
Mineral Resources ◽  
Weibull Model ◽  
Distribution Model ◽  
Forming Process ◽  
Grade Distribution ◽  
Economical Evaluation ◽  
Entropy Principle ◽  
Orderly State

The distribution of metallogenic elements grade is an effective index for the quantitatively economical evaluation of mineral resources. We have defined the information entropy as a measure of randomness of metallogenic elements grade distribution, assumed its primary distribution is in an extremely random situation, and deduced the density function of the primary distribution based on maximum entropy principle. Considering the fact that elements concentration goes from a non-orderly state to an orderly one in the ore-forming process, we added restraint parameters to the primary distribution model, got a two-parameter Weibull distribution model with embedded fractal features, and then fitted metallogenic element's grade distribution of Ag-Cu-Pb-Zn from a mine in China. The results show that the Weibull model is more effective than a lognormal model to describe elements distribution, and should be applied more broadly than common lognormal models in geology discipline.

An entropy concentration theorem: applications in artificial intelligence and descriptive statistics

1990 ◽  
Vol 27 (2) ◽  
pp. 303-313 ◽  
Author(s):  
Claudine Robert
Keyword(s):  
Artificial Intelligence ◽  
Maximum Entropy ◽  
Large Deviation ◽  
Maximum Entropy Principle ◽  
Statistical Modelling ◽  
Linear Constraints ◽  
Descriptive Statistics ◽  
Entropy Principle ◽  
Maximum Entropy Distribution ◽  
Mathematical Justification

The maximum entropy principle is used to model uncertainty by a maximum entropy distribution, subject to some appropriate linear constraints. We give an entropy concentration theorem (whose demonstration is based on large deviation techniques) which is a mathematical justification of this statistical modelling principle. Then we indicate how it can be used in artificial intelligence, and how relevant prior knowledge is provided by some classical descriptive statistical methods. It appears furthermore that the maximum entropy principle yields to a natural binding between descriptive methods and some statistical structures.

SINE ENTROPY FOR UNCERTAIN VARIABLES

2013 ◽  
Vol 21 (05) ◽  
pp. 743-753 ◽  
Author(s):  
KAI YAO ◽  
JINWU GAO ◽  
WEI DAI
Keyword(s):  
Maximum Entropy ◽  
Uncertainty Theory ◽  
Maximum Entropy Principle ◽  
Expected Value ◽  
Uncertain Variables ◽  
Entropy Principle

Entropy is a measure of the uncertainty associated with a variable whose value cannot be exactly predicated. In uncertainty theory, it has been quantified so far by logarithmic entropy. However, logarithmic entropy sometimes fails to measure the uncertainty. This paper will propose another type of entropy named sine entropy as a supplement, and explore its properties. After that, the maximum entropy principle will be introduced, and the arc-cosine distributed variables will be proved to have the maximum sine entropy with given expected value and variance.

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