Modeling Time Series Trends with Structural Changes using Multilayer Modular Regressions

Abstract

this study addresses the challenge of modeling technical and socio-economic systems whose dynamics evolve due to structural changes, resulting in shifts in the parameters of the trends that describe these dynamics. A trend model based on multilayer modular regression is proposed. The identification problem is formalized as a mixed 0-1 integer linear programming problem, solved using the least absolute deviations method. The efficacy of the proposed models is demonstrated through three case studies using time series that exhibit structural changes in their trends. The first case study focuses on population data from the Irkutsk region, while the second and third analyze freight and passenger rail transportation data. Unlike linear trend models, the multilayer modular regressions successfully identified all latent structural changes. Graphical illustrations demonstrate how increasing the number of regression layers enhances the quality of trend approximation. The most appropriate models for each case are presented as piecewise functions, enabling a meaningful interpretation of the results. The primary advantage of multilayer modular trend regressions is their ability to automatically detect time points at which trend directions change during the estimation process.