ANALYSIS AND IDENTIFICATION OF NEAR-PROPORTIONAL CHARACTERISTICS IN TIME SERIES

Staroverov Igor Nikolaevich

In today's environment, the exponential growth of information requires advanced data analysis techniques, especially for the analysis of nonlinear oscillations that exhibit stable structures. This study elucidates an empirical study that aims to decompose data to elucidate the dynamics driving fast and slow processes and to identify quasi-proportions in geometric progressions. Using stock data from Walmart, the study uses a methodology based on shift functions and metric spaces to facilitate the determination of the initial values and coefficients inherent in geometric progressions. This approach allows for an in-depth study of the rhythms inherent in geometric progressions, identifying close proportions and identifying critical points in time series. The methodological novelty lies in the use of functional analysis and specialized algorithms to clarify and evaluate the mathematical stability of the results. Empirical evidence validates the method's ability to comprehensively analyze complex time series and isolate key parameters, highlighting its essential relevance for data-driven research and its applicability across multiple sectors. Additionally, this study highlights the importance of multidimensional data analysis to improve forecasting accuracy and strategic decision making.

Keywords:empirical data, almost-proportions, geometric progression, shift functions, function spaces