Predicted Values from Models Based on Grey Theory

This program is designed to compute predicted values based on models established using grey theory, an emerging mathematical methodology that analyzes and processes incomplete or uncertain information to forecast future trends and patterns. The core mathematical model implemented is GM(1,1), which stands as one of the most fundamental and widely-used models in grey theory for characterizing the evolutionary trends of time series data. The GM(1,1) model demonstrates strong adaptability and prediction accuracy, making it applicable across diverse fields such as economics, environmental science, and healthcare. The program's algorithm involves generating accumulated sequences, establishing grey differential equations, and solving parameters through least squares estimation to produce forecasts. Beyond calculating predictions, the program incorporates model evaluation capabilities—including posterior variance tests and residual checks—to enhance forecasting precision and reliability. The implementation features multiple visualization tools that enable users to perform data analysis and present results through trend charts, prediction intervals, and error diagnostics. In essence, this program serves as a practical and robust tool that aids users in understanding and applying grey theory effectively, providing substantial support for future decision-making processes. Key functions include data preprocessing, model parameter optimization, and interactive plotting modules for comprehensive analytical workflows.