标题： 基于黎曼Zeta函数与FPAS模型（FPAS + $ζ$）混合集成的通货膨胀预测：周期灵活性、社会经济挑战和冲击，以及模型比较分析 显示英文标题

标题： 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

摘要： 通货膨胀预测是现代宏观经济学建模中的核心经济社会挑战，尤其是在周期性、结构性和冲击因素同时作用时。 传统的系统如FPAS和ARIMA往往难以应对周期性不对称性和意外波动。 本研究提出了一种混合框架（FPAS + $\zeta$），将结构宏观模型（FPAS）与从黎曼zeta函数得出的周期性成分 $\zeta(1/2 + i t)$相结合。 利用佐治亚州的宏观经济数据（2005-2024），从核心变量（如GDP、M3、政策利率）构建了一个非线性论证 $t$，并通过调制系数 $\alpha$最小化均方根误差进行混合预测校准。 基于傅里叶的频谱分析和隐马尔可夫模型（HMM）用于周期/相位识别，多准则AHP-TOPSIS方案比较了FPAS、FPAS + $\zeta$和ARIMA。 结果表明，FPAS + $\zeta$具有较低的均方根误差和优越的周期响应能力，并具备对冲击和制度转变的预警能力，表明对政策机构具有实际价值。 显示英文摘要

摘要： 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.