Finite-difference models application for short-term forecasting of the natural resource potential of the Perm region

The article is about a problem of mathematical modeling of the natural resource potential of the Perm Territory by 1st and 2nd order finite-difference models. Such models can obtain better forecasts of complex socio-economic processes in comparison with the traditionally used linear multiple regression models. A high quality model of the natural resource potential with forecast possibilities is one of the necessary conditions for the effective management of the natural resources of the region in order to ensure its sustainable economic development. Purpose of work. Aim of this work is work construction of finite-difference models of a natural resource potential complex indicators and an assessment of their prognostic properties. Materials and methods. Our research is based on Perm region statistical data for the period from 2001 to 2018. A multiple linear regression model is used as a comparison base. The natural resource potential complex indicator is calculated as a weighted sum of particular criteria characterizing the natural resources of the region. First and second order finite difference models are obtained by adding autoregressive terms of the first and second orders, respectively, to the multiple linear regression model. An estimation of the unknown parameters of the equations is carried out by a modified least squares method, which preserves the signs of the coefficients with the factors the same as in the original linear model. At the same time, the selection of explanatory factors and the assessment of the quality of the models are carried out based on the accuracy of the predicted values of the studied indicator. The results of the study. Components and factors of the natural resource potential is obtained, and a procedure for constructing finite-difference models is performed for three different time intervals: 2001-2018, 2001-2008, and 2008-2018. These intervals are chooseen because changes in the methodology for generating statistical data nearly 2008. Discussion and conclusions. The number of calculated predicted values was 18, and only in 4 out of 18 cases (22,2%) their quality is worse than forecasts obtained by the linear multiple model. So proposed modification of the multiple linear regression model with the addition of autoregressive terms makes it possible to improve the forecasting quality of the complex indicator of the natural resource potential of the region and, therefore, to make more effective decisions when managing its level.