Abstract
By using the phase analysis algorithm mechanism and the visualization and data analysis methods, the authors clearly show the resulting synergistic effect from the complex socio-economic processes research in the context of the triad results: the initial time series, a number of its increments and aggregated data. The article is devoted to the adaptation of mathematical methods of nonlinear dynamics and the description of the tool for obtaining pre-forecast information about complex economic processes, in particular, the phase analysis algorithm testing in the research of the time series of the tourist flow to the Dombai ski village of the Karachay-Cherkess Republic. Phase analysis is the method for studying local fluctuations in a time series that are asymmetric, irregular, and have an unstable period.
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