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

Inflation forecasting is one of the main socio-economic challenges in modern macroeconomic modeling, especially when cyclical, structural, and shock factors act simultaneously in the system. Traditional forecasting systems, such as Forecasting and Policy Analysis System (FPAS) and Autoregressive Integrated Moving Average (ARIMA), often fail to provide an adequate analysis of cyclical asymmetry and unexpected fluctuations. The presented study proposes a hybrid approach that combines a structural macroeconomic model (FPAS) and the cyclical components of the Riemann zeta function, creating a completely new forecasting framework (FPAS + ζ). The study is the first to use the cyclical components of the Riemann zeta function in practice within a structural macroeconomic model, which significantly increases the accuracy of the forecast and the ability to adapt to policy instruments. The uniqueness of the model lies in the fact that it reduces the forecast error and increases the system's responsiveness to cyclical and shock conditions. The cyclical characteristic is modeled based on the macroeconomic indicators of Georgia (2005–2024), using a nonlinear argument t, on which the cyclical adjustment is based on the formula ζ(0.5 + i·t). The forecast is modulated by an α-coefficient, which is optimized by the principle of Root Mean Square Error (RMSE) minimization. The model also combines Fourier decomposition for spectral analysis and the hidden Markov model for phase identification, which provides a deep analysis of inflation fluctuations over time. The implementation of this hybrid inflation forecasting framework will make a significant contribution to solving socio-economic challenges, thereby increasing the accuracy of forecasting and flexibility at the practical level of policy.