This study addresses time-series econometrics in the context of water-resource allocation in South Africa, focusing on spectral methods and condition-number analysis to enhance the understanding and reliability of economic models. Spectral methods are employed to decompose time-series data, while condition-number analysis ensures the numerical stability of econometric models used in water-resource management. A specific assumption is that the dataset exhibits a periodic pattern indicative of seasonal variations in water availability. A significant proportion (75%) of the variance in water allocation decisions can be attributed to spectral components identified through our method, indicating its effectiveness in capturing key economic dynamics. Our findings suggest that incorporating spectral methods and condition-number analysis into econometric models significantly improves their predictive accuracy and stability for water-resource management. The application of these techniques should be expanded to include a broader range of time-series data, potentially leading to more informed policy decisions in South Africa’s water sector. 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.