演講者：李詠玄教授 (逢甲大學應用數學系)

日   期：2026 年 03 月 25 日（星期三）13:30

地   點：國立高雄大學理學院 408 室

講   題：A Dynamical System Approach for Modeling Nonstationary Financial Time Series

摘   要：

Nonstationary time series governed by nonlinear dynamics present substantial challenges to conventional modeling frameworks. This study proposes a hybrid dynamical system framework that integrates two differential equation–based models to characterize complex temporal evolution. The framework combines the relative growth–parabola model (RGPM) to describe nonlinear growth dynamics and the new price reversion model (nPRM) to capture mean-reversion behavior.

To address the inherent non-differentiability and noise characteristics commonly observed in real-world time series, uniform phase empirical mode decomposition (UPEMD) is employed as a preprocessing procedure for signal refinement. The hybrid structure primarily adopts RGPM and switches to nPRM when the associated variable transformation becomes invalid, thereby avoiding singularities in the analytical solution. The theoretical formulation guarantees existence and uniqueness of solutions while preserving structural interpretability.

Empirical evaluation indicates that the proposed hybrid dynamic framework substantially improves predictive performance compared with recurrent neural network benchmarks, achieving markedly lower forecasting error. Beyond financial applications, the framework offers a rigorous and generalizable methodology for modeling nonstationary nonlinear dynamics in domains such as physics, climate science, and engineering systems.