Forecasting Inflation Based on Hybrid Integration of the Riemann Zeta Function and the FPAS Model (FPAS + $\zeta$): Cyclical Flexibility, Socio-Economic Challenges and Shocks, and Comparative Analysis of Models

Inflation forecasting is a core socio-economic challenge in modern macroeconomic modeling, especially when cyclical, structural, and shock factors act simultaneously. Traditional systems such as FPAS and ARIMA often struggle with cyclical asymmetry and unexpected fluctuations. This study proposes a hybrid framework (FPAS + $\zeta$) that integrates a structural macro model (FPAS) with cyclical components derived from the Riemann zeta function $\zeta(1/2 + i t)$. Using Georgia's macro data (2005-2024), a nonlinear argument $t$ is constructed from core variables (e.g., GDP, M3, policy rate), and the hybrid forecast is calibrated by minimizing RMSE via a modulation coefficient $\alpha$. Fourier-based spectral analysis and a Hidden Markov Model (HMM) are employed for cycle/phase identification, and a multi-criteria AHP-TOPSIS scheme compares FPAS, FPAS + $\zeta$, and ARIMA. Results show lower RMSE and superior cyclical responsiveness for FPAS + $\zeta$, along with early-warning capability for shocks and regime shifts, indicating practical value for policy institutions.