SYNTHESIS OF LAG AND INTEGRAL MODELS OF ECONOMIC AND ECOLOGICAL PROCESSES
DOI:
https://doi.org/10.31618/ESSA.2782-1994.2021.1.76.194Keywords:
distributed lag, exogenous and endogenous variables, degenerate kernel, Fredholm integral equation, resolvent, eigenvalues of the integral operator.Abstract
In this paper, the authors propose to model the dynamic processes of economics and ecology not by differential, but by integral Fredholm (or Volterra) equations. Since with this approach, the overwhelming majority of simultaneous values of indicators representing exogenous and endogenous variables of the corresponding economic and mathematical models are considered, the authors attempt to synthesize distributed lag models (continuous and discrete) with Fredholm (Volterra) integral equations. The integral core, which is part of the transforming operator, transfers its accumulating action, transforming, in essence, an exogenous indicator into an endogenous one. Three schemes are proposed, according to which the resulting integral indicator is realized in relation to a stimulus with a lagging argument (lag). The synthesis of the distributed lag model and the model, the apparatus of which is the Fredholm and Volterra integral equations, will increase the reliability (probability of reliability) of the forecast estimates of the economic indicators of the models.
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