Rational dimension of a basis of a regression model for adaptive short-term forecasting the state of a discrete nonstationary dynamic system
Authors: Glazyrin Alexander S. , Bolovin Evgeniy V. , Arkhipova Olga V. , Kovalev Vladimir Z. , Khamitov Rustam N. , Kladiev Sergey N. , Filipas Alexander A. , Timoshkin Vadim V. , Kopyrin Vladimir A. , Beliauskene Evgeniia A. 
Published: November 2023

Relevance. Today, there are many methodologies for predicting power consumption of various objects. However, there is no a general methodology that is suitable for all types of energy systems, including the sectoral characteristics of small northern settlements and other objects with the stochastic nature of electricity consumption schedules. At the same time, during the development of problem-oriented forecasting methods, it is necessary to take into account computational and statistical features of forecasted time series to the maximum and apply them adequately. The mentioned circumstance prompts the creation of criteria-indicators that allow evaluating the quality of the applied model for solving the forecasting problem, correctness of its construction and correctness of applying a priori information about the object and its physical properties.Aim. Develop and apply the criteria-indicators, which allow evaluating the quality of the forecast regression model and the influence of the dimensionality of such model base on a forecasting error. Methods. The choice of rational dimensionality of the regression model basis for the adaptive forecasting problem is based on the known and developed criteria-indicators. The main provisions of such criteria-indicators were formulated, which provide an assessment of the quality of conditioning of an equivalent square matrix, the presence of uninformative elements of the matrix, and linear dependence of the columns. Results. Based on the analysis of criteria-indicators, the authors selected a rational dimension of the regression model basis for the problem of adaptive short-term forecasting of the state of discrete non-stationary dynamic systems. Conclusions. The authors have previously selected the most promising criteria-indicators and developed a normalized difference factor of diagonal predominance. This allows us to evaluate the influence of the basis size change on the regression model quality when building an approach of adaptive short-term forecasting of electricity consumption by autonomous power systems of small northern settlements on the basis of regression analysis methods. Based on the analysis of criteria-indicators the authors obtained information about the influence of the regression model basis dimension on the forecasting problem solution error. The authors stated the further stages of research to reduce this error. The paper introduces and describes one of the ways to improve the forecasting model quality. The dependence of the forecasting error on the size of the regression model basis were revealed; the criteria-indicators considered in the article were successfully applied. It is confirmed that the pre-selected and developed criteria-indicators make it possible, at the stage of compiling an equivalent square matrix and performing preliminary actions on it, to track changes within the matrix. The changes will lead to improvement in the solution of the problem of adaptive short-term forecasting.