GM(1,1) Grey Prediction Model: Algorithm Explanation and Implementation Guide

The GM(1,1) grey prediction model serves as a versatile forecasting tool applicable to diverse prediction scenarios. It exhibits outstanding performance in short-term electricity load forecasting while maintaining capability for mid-to-long-term predictions. However, model accuracy inversely correlates with forecast duration, requiring careful consideration of temporal scope in implementation.

The model's core algorithm involves constructing a first-order differential equation (the '1,1' denotes first-order, one-variable) through cumulative data generation from limited samples. Key computational steps include: 1) Accumulated Generating Operation (AGO) transformation to strengthen data regularity, 2) parameter estimation using least squares method for model coefficients, and 3) inverse AGO restoration for prediction outputs. The iterative prediction mechanism continuously updates the model by incorporating new data points, enabling dynamic forecasting through recursive calculations.

Beyond power system applications, the GM(1,1) model finds extensive implementation in financial forecasting, economic trend analysis, and environmental modeling. Its mathematical foundation allows efficient coding in platforms like MATLAB or Python, typically requiring 15-20 lines of core implementation code. The model's adaptability to small datasets (minimum 4 data points) and computational efficiency make it particularly valuable for scenarios with limited historical information.