Polymodeling of time series structures, neighborhood of residuals distribution, wavelet transformation for meso-dynamics assessment

Subject. The article provides the results of meso-dynamics analysis of main twelve industries, based on monthly data for 82 Russian regions, from January 2005 till December 2020.Objectives. The purpose of the study is to address the problem of balanced and stable spatial development of Russia’s regions and Russia, which requires modeling of adequate tools and forecasting nonlinear mesodynamics.Methods. The study follows the econophysics methodology.Results. We consider additive and multiplicative interactions of regular time series components between each other and the residuals, thus expanding the scope of tools application for the variety of considered industries and their models. Using the common and new trend models, we analyze structural changes, introduce the topological measure of proximity to the neighborhood of residuals with heavy-tailed distribution, which is estimated by median values of trends and cycles for regular components. The traditional time series decomposition (by trend, cycle, seasonality, and residual) is supplemented by our unique complex of wavelet transformations, which forms the models of cycles, using auto regression. We obtained representative and time-synchronized analytical estimates of regular components of industries’ dynamics for meso- and macro-indicators of the Russian economy that have higher accuracy than the known results for the accuracy of modeling and forecasting.Conclusions. The offered methodology and tools enable a more adequate analysis of non-linear dynamics of regions’ middle-term development. They help shift to growth point identification, create the atlas of economic industrial cycles, analyze stages of bifurcations and scenario predictive planning.