Relative fractional dynamics of stock markets

Machado, J. A. Tenreiro; Lopes, António M.

doi:10.1007/s11071-016-2980-1

Cited by 49 publications

(6 citation statements)

References 40 publications

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“…The proposed criteria can be important for specifying the class of differential and integral operators that can be used to describe economic processes with memory of power-law type. As a result, the suggested approach can be used for constructing models of real financial and economic processes, [ 81 , 82 , 83 , 84 , 85 , 86 , 87 , 88 , 89 ] and [ 19 , 25 , 26 , 27 , 28 , 29 , 30 , 89 , 90 , 91 , 92 , 93 , 94 , 95 ], in which memory effects are manifested. Note that phenomenological economic process are described by computer simulation of the economies of Spain, Portugal, France, Italy are presented by I. Tejado, D. Valerio, E. Perez, and N. Valerio in the works [ 89 , 90 , 91 , 92 ].…”

Section: Discussionmentioning

confidence: 99%

Criterion of Existence of Power-Law Memory for Economic Processes

Tarasova

2018

Entropy

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Abstract:In this paper, we propose criteria for the existence of memory of power-law type (PLT) memory in economic processes. We give the criterion of existence of power-law long-range dependence in time by using the analogy with the concept of the long-range alpha-interaction. We also suggest the criterion of existence of PLT memory for frequency domain by using the concept of non-integer dimensions. For an economic process, for which it is known that an endogenous variable depends on an exogenous variable, the proposed criteria make it possible to identify the presence of the PLT memory. The suggested criteria are illustrated in various examples. The use of the proposed criteria allows apply the fractional calculus to construct dynamic models of economic processes. These criteria can be also used to identify the linear integro-differential operators that can be considered as fractional derivatives and integrals of non-integer orders.

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Section: Discussionmentioning

confidence: 99%

Criterion of Existence of Power-Law Memory for Economic Processes

Tarasova

2018

Entropy

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“…During the last decades FC has become a popular tool [29][30][31], and new areas of application have emerged. The modeling finance [32] and economy [18,21,22,26,[33][34][35] phenomena became of particular relevance.…”

Section: The Fractional Calculusmentioning

confidence: 99%

Fractional Dynamics and Pseudo-Phase Space of Country Economic Processes

2020

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In this paper, the fractional calculus (FC) and pseudo-phase space (PPS) techniques are combined for modeling the dynamics of world economies, leading to a new approach for forecasting a country’s gross domestic product. In most market economies, the decline of the post-war prosperity brought challenging rivalries to the Western world. Considerable social, political, and military unrest is today spreading in major capital cities of the world. As global troubles including mass migrations and more abound, countries’ performance as told by PPS approaches can help to assess national ambitions, commercial aggression, or hegemony in the current global environment. The 1973 oil shock was the turning point for a long-run crisis. A PPS approach to the last five decades (1970–2018) demonstrates that convergence has been the rule. In a sample of 15 countries, Turkey, Russia, Mexico, Brazil, Korea, and South Africa are catching-up to the US, Canada, Japan, Australia, Germany, UK, and France, showing similarity in many respects with these most developed countries. A substitution of the US role as great power in favor of China may still be avoided in the next decades, while India remains in the tail. The embedding of the two mathematical techniques allows a deeper understanding of the fractional dynamics exhibited by the world economies. Additionally, as a byproduct we obtain a foreseeing technique for estimating the future evolution based on the memory of the time series.

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“…Indeed, the models based on classical calculus often fail to explain the genetic and inheritance properties of many complex systems having anomalous dynamics, whereas the fractional derivatives and integrals allow for a simpler and more accurate representation of their features. Due to the above-mentioned properties, fractional order integral equations (FOIEs) have been used in many engineering and physics fields to investigate complex systems, for instance, viscoelasticity and traffic models, temperature and motor control, and solid mechanics [4][5][6][7][8]. However, FOIEs pose difficulties in achieving their accurate analytical solution and numerical techniques have to be used in order to derive useful result [9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Hybridization of Block-Pulse and Taylor Polynomials for Approximating 2D Fractional Volterra Integral Equations

et al. 2022

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This paper proposes an accurate numerical approach for computing the solution of two-dimensional fractional Volterra integral equations. The operational matrices of fractional integration based on the Hybridization of block-pulse and Taylor polynomials are implemented to transform these equations into a system of linear algebraic equations. The error analysis of the proposed method is examined in detail. Numerical results highlight the robustness and accuracy of the proposed strategy.

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Relative fractional dynamics of stock markets

Cited by 49 publications

References 40 publications

Criterion of Existence of Power-Law Memory for Economic Processes

Criterion of Existence of Power-Law Memory for Economic Processes

Fractional Dynamics and Pseudo-Phase Space of Country Economic Processes

Hybridization of Block-Pulse and Taylor Polynomials for Approximating 2D Fractional Volterra Integral Equations

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