(untitled) (Journal of Mathematics Mechanics and Computer Science, 2026)
Financial systems today handle massive real-time transaction volumes, where anomalies are rare, time-sensitive, and masked by stochastic noise. Traditional detection methods often fail to address the dynamic nature of fraud or provide the interpretability required by regulated financial sectors. This paper develops an interpretable hybrid framework for anomaly detection, integrating numerical optimization within state-space models and ARIMAX/SARIMAX architectures. The proposed model effectively captures evolving temporal dependencies and structural shifts in transaction data. By decomposing signals into baseline trends and exogenous residuals, the framework provides a transparent mathematical basis for every flagged anomaly, ensuring auditability. The system’s performance is rigorously validated using the Precision@K metric and a comprehensive cost-utility analysis. Results demonstrate that this numerical optimization-based approach minimizes false positives while identifying high-risk transactions. Ultimately, this framework offers a scalable, real-time solution that bridges the gap between high predictive power and the transparency necessary for financial forensic analysis.