Gray Prediction Model Programming in MATLAB (Based on GM(1,1) Model)

I have developed a gray prediction model using MATLAB programming language based on the GM(1,1) model framework. The implementation primarily utilizes MATLAB's matrix operations and differential equation solving capabilities to establish the prediction model. This model was originally created to handle specific data processing requirements, featuring straightforward implementation logic and practical applicability. The core algorithm involves accumulating generation operations (AGO) to transform original data sequences, followed by establishing gray differential equations using least squares fitting. The model's main functionality focuses on predicting the next sequential data point, but the code architecture allows for extension to generate multiple future predictions by modifying the prediction horizon parameter. Beyond single-point forecasting, this implementation can analyze data trends and patterns through residual testing and posterior variance ratio calculations, providing valuable insights for data analysis and decision-making processes. For enhanced prediction accuracy, users can incorporate more historical data into the training set or implement additional validation methods such as rolling forecasts or comparison with alternative prediction models like ARIMA or neural networks to verify result reliability. The modular code design facilitates easy integration of these enhancements.