Time-series econometrics is a crucial tool for forecasting power-grid behaviour in Nigeria, where accurate predictions are essential for grid stability and reliability. This paper introduces a novel approach to analyse the stability and derive convergence proofs for econometric models applied to power-grid data. We establish an assumption that all model parameters are non-negative, ensuring realistic forecasts. The analysis employs a specific error term property, which guarantees stability under certain conditions. Our findings indicate that by applying these methodologies, we can achieve more reliable and consistent predictions of power-grid behaviour over time. The developed methods provide a solid foundation for improving the accuracy and reliability of future power-grid forecasts in Nigeria. Future research should validate these models using real-world data to ensure their practical applicability. Stability Analysis, Convergence Proofs, Time-Series Econometrics, Power-Grid Forecasting The analytical core is $\hat{y}_t=\mathcal{F}(x_t;\theta)$ with $\hat{\theta}=argmin_{\theta}L(\theta)$, and convergence is established under standard smoothness conditions.