Community health centers (CHCs) in Ethiopia play a pivotal role in delivering healthcare services to underserved populations. However, their performance and efficiency are often underreported. A time-series analysis was conducted using ARIMA (AutoRegressive Integrated Moving Average) model to forecast yield improvement metrics over a five-year period. Robust standard errors were calculated for uncertainty quantification. The ARIMA model demonstrated an R² value of 0.85 and a confidence interval of ±10% for the forecasted yield improvements, indicating moderate accuracy in future projections. This study confirms the utility of time-series models in evaluating CHC performance and provides a methodological framework that can be applied to other healthcare systems. Further research should explore multi-model comparisons and incorporate additional contextual variables for enhanced predictive power. Community Health Centers, Time-Series Models, Forecasting Yield Improvement, ARIMA Treatment effect was estimated with $\text{logit}(p_i)=\beta_0+\beta^\top X_i$, and uncertainty reported using confidence-interval based inference.