A Novel Grey Model with Persistent Homology-Based Feature with Its Applications

Accurate forecasting of coal consumption and production is vital for strategic energy planning in the Philippines, where coal remains a primary energy source with a pronounced long-term upward trend. We propose a Topological Data-Augmented Grey Model (TDA-GM(1,1)), a first-order differential grey model that extends the classical GM(1,1) by integrating L1-norms of persistence landscapes from persistent homology as a topological driving term, to improve forecasting precision. By incorporating these topological features, TDA-GM(1,1) captures the complex, nonlinear dynamics inherent in coal consumption and production data influenced by economic and policy factors. Using historical annual data from 1977–2016 for training and 2017–2020 for testing, we evaluate performance via MSE, RMSE, MAE, and both in-sample and out-of-sample MAPE and compare TDA-GM(1,1) with benchmark models GM(1,1), DGM(1,1), ARIMA, Exponential Smoothing, and Linear Regression. We find that TDA-GM(1,1) achieves the lowest out-of-sample MAPE for both coal consumption and production while remaining competitive in ex-ante variance diagnostics. This model adapts to nonlinear trends, making it valuable for policymakers managing energy resources and planning. This study highlights the potential of TDA-enhanced grey models for small-sample energy time series and the broader applicability of TDA in forecasting complex dynamics.