Tarasov Vasily E, Tarasova Valentina V
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119991 Moscow, Russia.
Lomonosov Moscow State University Business School, Lomonosov Moscow State University, 119991 Moscow, Russia.
Entropy (Basel). 2018 May 29;20(6):414. doi: 10.3390/e20060414.
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.
在本文中，我们提出了经济过程中幂律型（PLT）记忆存在的标准。通过与长程α相互作用的概念进行类比，我们给出了时间上幂律长程相依性存在的标准。我们还利用非整数维的概念提出了频域中PLT记忆存在的标准。对于一个已知内生变量依赖于外生变量的经济过程，所提出的标准使得识别PLT记忆的存在成为可能。在各种示例中说明了所建议的标准。使用所提出的标准允许应用分数阶微积分来构建经济过程的动态模型。这些标准还可用于识别可被视为非整数阶分数导数和积分的线性积分 - 微分算子。
