MATLAB Source Code for Grey Prediction GM(1,1) Model with Accuracy Validation

This MATLAB source code implements the Grey Prediction GM(1,1) model, covering both model establishment and calculation of accuracy validation indicators c and p. The GM(1,1) model construction begins with accumulating generation operations on historical data sequences. The implementation involves creating first-order accumulated generating operations (1-AGO) to weaken data randomness, followed by constructing grey differential equations using the least squares method. Key computational steps include building the background values matrix and solving for development coefficients (a) and grey action quantities (b) through matrix operations. The prediction model then generates restored values through inverse accumulated generating operations. For accuracy validation, the code calculates two critical indicators: c (mean variance ratio) and p (small error probability). The c indicator evaluates the mean square error ratio between residual and original sequences, while p assesses the probability of small prediction errors relative to a specified threshold. The implementation involves computing residual sequences, mean values, and statistical distributions to determine model reliability. These metrics provide quantitative assessment of prediction accuracy and model performance stability. The source code provides a complete framework for grey prediction modeling, featuring data preprocessing functions, coefficient calculation algorithms, prediction generators, and automated validation routines. Users can input historical data sequences to establish prediction models and obtain comprehensive accuracy reports for future trend forecasting applications.