Topological Data Analysis (TDA) is a method used to analyse complex data sets by constructing topological structures such as simplicial complexes and persistent homology. We employ a TDA framework utilising persistent homology to analyse spatially distributed agricultural yield data. We assume stationarity in the underlying data-generating process and use the Vietoris-Rips complex as our topological structure. The main property we rely on is that under certain conditions, the persistence diagrams converge to a stable distribution. We observed significant variability in yield patterns across different regions of Nigeria, with some areas showing consistent high yields over multiple years while others exhibited unpredictable fluctuations. Our analysis confirms the utility of TDA for agricultural yield prediction and highlights the importance of considering regional-specific factors. The asymptotic convergence property ensures that our predictions are reliable over extended periods. Further research should include validation with additional datasets and exploration of temporal dynamics to enhance predictive accuracy. Topological Data Analysis, Agricultural Yield Prediction, Nigeria, Asymptotic Convergence, Identifiability Checks 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.