The article deals with the selection and development of effective methods for studying the relationship and forecasting economic indicators. It is shown that despite the fact that the most frequently used tool for solving these problems is the use of regression dependencies, in some cases, for example, for processes that do not have clearly defined and predetermined trends, or, in the case of studies of unstable processes, as well as for requirements of increased accuracy of analysis, it makes sense to use, adapt or develop methods to obtain appropriate analytical expressions. The analysis of various methods is given. The use of a method based on the expansion of functions into polynomials orthonormalized on the orthogonality interval, which was considered by the author in previous works, is proposed. This article focuses on the reasonable choice of the number of orthonormal polynomials, consistent with a given accuracy of the approximation of the original function based on the properties of the Gram determinant. Directions for further research are indicated.
forecasting, approximation, interpolation, orthonormal polynomials, Gram determinant
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