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Open AccessEditor’s ChoiceArticle

Criterion of Existence of Power-Law Memory for Economic Processes

1
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
2
Lomonosov Moscow State University Business School, Lomonosov Moscow State University, 119991 Moscow, Russia
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Author to whom correspondence should be addressed.
Entropy 2018, 20(6), 414; https://doi.org/10.3390/e20060414
Received: 23 April 2018 / Revised: 22 May 2018 / Accepted: 26 May 2018 / Published: 29 May 2018
(This article belongs to the Special Issue Power Law Behaviour in Complex Systems)
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. View Full-Text
Keywords: power-law memory; long memory; economic dynamics; multiplier with memory; accelerator with memory; fractional derivative; fractional integral power-law memory; long memory; economic dynamics; multiplier with memory; accelerator with memory; fractional derivative; fractional integral
MDPI and ACS Style

Tarasov, V.E.; Tarasova, V.V. Criterion of Existence of Power-Law Memory for Economic Processes. Entropy 2018, 20, 414.

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