Model for forecasting tax risks based on the combination of approximation methods and differential game theory models

Abstract

The relevance of the study is determined by the transformation of the modern tax administration system, the strengthening of digital control, the automation of tax monitoring procedures, and the implementation of a risk-oriented approach in the activities of regulatory authorities. The purpose of the study is to substantiate a mathematical approach to forecasting enterprise tax risks based on the combination of interpolation analogues of operators generated by Fourier series and differential game theory models for the formalization of interrelated tax time series. The methodological basis of the research includes methods of mathematical modeling, time series analysis, interpolation and approximation methods, interpolation analogues of Abel–Poisson operators, as well as approaches of differential game theory for describing the mutual influence of tax indicators in dynamics. During the study, tax burden, tax debt, tax adjustments, penalty sanctions, and enterprise liquidity were considered as a system of interconnected time series forming the taxpayer’s risk profile. As a result of the study, an adaptive mathematical model for forecasting tax risks was proposed, providing the possibility of simultaneous analysis and iterative forecasting of several interrelated tax indicators. The expediency of using interpolation analogues of operators generated by Fourier series for considering the cyclicality and seasonality of tax processes, as well as differential game theory models for describing the dynamic interdependence of tax indicators, was substantiated. It was established that the transition from a continuous to a discrete form of the model makes it possible to adapt it to the real conditions of the tax compliance system, within which financial and tax information is generated in specific reporting periods. The practical value of the obtained results lies in the possibility of applying the proposed model in tax compliance systems, digital tax analytics, ERP systems, and accounting information platforms of enterprises. The proposed approach creates the basis for the automation of tax monitoring, early detection of risk tendencies, forecasting of tax debt, and support of managerial decision-making in the field of tax planning and internal control.