Dynamic Keynesian Model of Economic Growth with Memory and Lag

Tarasova, Valentina V.

doi:10.3390/math7020178

Cited by 24 publications

(32 citation statements)

References 56 publications

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“…C,0+ f (τ), and the kernel is the probability density function of the gamma distriburion (for details, see the Section 7 of the article [29] and the papers [30][31][32]). Such a choice is necessary to describe the simultaneous presence of two such phenomena as distributed lag and fading memory.…”

Section: Remarkmentioning

confidence: 99%

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Fractional Derivatives and Integrals: What Are They Needed For?

Tarasova

2020

Mathematics

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The question raised in the title of the article is not philosophical. We do not expect general answers of the form “to describe the reality surrounding us”. The question should actually be formulated as a mathematical problem of applied mathematics, a task for new research. This question should be answered in mathematically rigorous statements about the interrelations between the properties of the operator’s kernels and the types of phenomena. This article is devoted to a discussion of the question of what is fractional operator from the point of view of not pure mathematics, but applied mathematics. The imposed restrictions on the kernel of the fractional operator should actually be divided by types of phenomena, in addition to the principles of self-consistency of mathematical theory. In applications of fractional calculus, we have a fundamental question about conditions of kernels of fractional operator of non-integer orders that allow us to describe a particular type of phenomenon. It is necessary to obtain exact correspondences between sets of properties of kernel and type of phenomena. In this paper, we discuss the properties of kernels of fractional operators to distinguish the following types of phenomena: fading memory (forgetting) and power-law frequency dispersion, spatial non-locality and power-law spatial dispersion, distributed lag (time delay), distributed scaling (dilation), depreciation, and aging.

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Section: Remarkmentioning

confidence: 99%

“…The fractional derivatives and integrals of non-integer orders, in which lag (time delay) is described by continuous probability distributions, were proposed in [29] (pp. 148-154), and used in macroeconomic models [30][31][32]. An example of fractional operators with distributed lag is also suggested in the Section 7 of the paper [29] (pp.…”

Section: Statementmentioning

confidence: 99%

Fractional Derivatives and Integrals: What Are They Needed For?

Tarasova

2020

Mathematics

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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%

“…Using the equivalence of fractional differential equations and the Volterra integral equations they obtained discrete maps with memory that were exact discrete analogs of fractional differential equations of economic processes. Tarasov and Tarasova [22] designed a model of economic growth with fading memory and continuous distribution of delay time. Their approach can be considered as a generalization of the standard Keynesian macroeconomic model.…”

Section: Introductionmentioning

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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“…Nowadays, fractional calculus, fractional-order systems, fractional-order processes and fractional signal processing techniques and their real world applications in various areas have been described in several works [3][4][5][6][7][8]. Long memory has been observed even in economics [9]. A very useful application of the fractional calculus in the time series analysis of heart rate variability was shown in [10].…”

Section: Introductionmentioning

confidence: 99%

Fractional Calculus as a Simple Tool for Modeling and Analysis of Long Memory Process in Industry

Petráš

Terpák

2019

Mathematics

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This paper deals with the application of the fractional calculus as a tool for mathematical modeling and analysis of real processes, so called fractional-order processes. It is well-known that most real industrial processes are fractional-order ones. The main purpose of the article is to demonstrate a simple and effective method for the treatment of the output of fractional processes in the form of time series. The proposed method is based on fractional-order differentiation/integration using the Grünwald-Letnikov definition of the fractional-order operators. With this simple approach, we observe important properties in the time series and make decisions in real process control. Finally, an illustrative example for a real data set from a steelmaking process is presented.

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Dynamic Keynesian Model of Economic Growth with Memory and Lag

Cited by 24 publications

References 56 publications

Fractional Derivatives and Integrals: What Are They Needed For?

Fractional Derivatives and Integrals: What Are They Needed For?

Fractional Dynamics and Pseudo-Phase Space of Country Economic Processes

Fractional Calculus as a Simple Tool for Modeling and Analysis of Long Memory Process in Industry

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