Method of Wavelet Analysis of Time Series to Assess the Effectiveness of the Country’s Energy Security

This article addresses the problems of energy security at the level of Russian regions, which is a particularly urgent in modern economic conditions characterized by global digitalization processes. In this case, the problem arises the need to develop mathematical tools for planning and assessing energy security in conditions of high uncertainty and fluctuations of the studied parameters of the external environment. The paper presents the mathematical justification for the use of wavelet analysis and the construction of spaces of scaling functions in order to obtain the theorem of multifunctional analysis of economic parameters and indicators of regional energy security, based on many intervals and determining the corresponding wavelet spaces.