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

Serhii Lupenko and Andrii Horkunenko ()
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Serhii Lupenko: Department of Informatics, Opole University of Technology, 45-758 Opole, Poland
Andrii Horkunenko: Department of Medical Physics of Diagnostic and Therapeutic Equipment, I. Horbachevsky Ternopil National Medical University, 46000 Ternopil, Ukraine

Forecasting, 2025, vol. 7, issue 2, 1-26

Abstract: 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.

Keywords: mathematical modeling; cyclic economic processes; cyclic random process; rhythm-adaptive statistical processing; forecasting (search for similar items in EconPapers)
JEL-codes: A1 B4 C0 C1 C2 C3 C4 C5 C8 M0 Q2 Q3 Q4 (search for similar items in EconPapers)
Date: 2025
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