Stochastic Model and Rhythm-Adaptive Technologies of Statistical Analysis and Forecasting of Economic Processes with Cyclic Components

This article presents a mathematical model of cyclical economic processes, formulated as the sum of a deterministic polynomial function and a cyclic random process that simultaneously captures trend, stochasticity, cyclicity, and rhythm variability. Building on this stochastic framework, we propose rhythm-adaptive statistical techniques for estimating the probabilistic characteristics of the cyclic component; by adjusting to rhythm changes, these techniques improve estimation accuracy. We also introduce a forecasting procedure that constructs a system of rhythm-adaptive confidence intervals for future cycles. The effectiveness of the model and associated methods is demonstrated through a series of computational experiments using Federal Reserve Economic Data. Results show that the rhythm-adaptive forecasting approach achieves mean absolute errors less than half of those produced by a comparable non-adaptive method, underscoring its practical advantage for the analysis and prediction of cyclic economic phenomena.