Improved Algorithm for Residual Grey Model with Code Implementation

The improved algorithm for residual grey model serves as an optimization solution for traditional grey prediction models, primarily enhancing prediction accuracy through secondary modeling of residual sequences. This algorithm demonstrates high practical value in time series forecasting, particularly suitable for small-sample and information-scarce data scenarios.In MATLAB implementation, this typically involves creating separate functions for GM(1,1) modeling and residual processing. The core improvement approach consists of three key phases: First is the preliminary prediction stage using the original grey model. The conventional GM(1,1) model performs initial modeling on the raw sequence to generate primary prediction results. The critical aspects involve optimized background value calculation and appropriate initial condition selection. In code implementation, this requires careful handling of cumulative generation operations and parameter estimation using least squares method. Next comes the residual sequence analysis and processing phase. Characteristic analysis is conducted on the residual sequence generated from the initial prediction, with appropriate transformations (such as logarithmic or translation transformations) applied to improve smoothness and randomness. This process significantly enhances the modelability of residual sequences. Programmatically, this stage involves implementing transformation functions and statistical analysis of residual patterns. Finally, the residual correction model construction phase employs improved algorithms for secondary modeling of processed residual sequences. Common enhancements include introducing weighting factors and optimizing background value construction. The final step combines correction terms with initial prediction results to obtain more accurate comprehensive forecasts. Code implementation would require developing adaptive weighting mechanisms and optimized parameter estimation functions. This improved algorithm effectively overcomes the traditional grey model's limitation in forecasting fluctuating data through dual modeling mechanisms. Test results demonstrate significantly reduced prediction errors across various scenarios, with outstanding performance particularly on datasets exhibiting trend and periodic characteristics. In practical applications, attention must be paid to data preprocessing importance, including outlier handling and dimension unification steps. Meanwhile, parameter selection for the residual correction model requires optimization adjustments based on specific data characteristics to achieve optimal prediction performance. The algorithm can be implemented using iterative optimization techniques and cross-validation methods for parameter tuning.