Fractional dynamics and pseudo-phase space of country economic processes

José A. Tenreiro Machado, Maria Eugénia Mata, António M. Lopes

Research output: Contribution to journalArticle

Abstract

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.
Original languageEnglish
Pages (from-to)1-17
JournalMathematics
Volume8
Issue number1
DOIs
Publication statusPublished - Jan 2020

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Economic processes
World economy
Military
France
Fractional calculus
By-products
Russia
Aggression
Rivalry
Turning point
South Africa
Oil shocks
Germany
Brazil
Global environment
Modeling
Hegemony
Developed countries
Mexico
Japan

Keywords

  • fractional calculus
  • pseudo-phase space
  • economy
  • system modeling

Cite this

Tenreiro Machado, José A. ; Mata, Maria Eugénia ; Lopes, António M. / Fractional dynamics and pseudo-phase space of country economic processes. In: Mathematics. 2020 ; Vol. 8, No. 1. pp. 1-17.
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Fractional dynamics and pseudo-phase space of country economic processes. / Tenreiro Machado, José A.; Mata, Maria Eugénia; Lopes, António M.

In: Mathematics, Vol. 8, No. 1, 01.2020, p. 1-17.

Research output: Contribution to journalArticle

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