Combined Forecasting with Discrete Grey Prediction Model and AR Prediction Model

The combined forecasting approach utilizing Discrete Grey Prediction Model and AR Prediction Model, implemented through MATLAB, has emerged as a significant research focus in recent years. These models employ sophisticated mathematical algorithms to analyze temporal data patterns and generate accurate predictions, demonstrating remarkable effectiveness across diverse domains including finance, economics, and meteorological forecasting. The Discrete Grey Prediction Model, rooted in grey system theory pioneered by Chinese mathematician Deng Julong during the 1980s, operates through differential equation modeling of limited data sequences. In MATLAB implementation, this typically involves data preprocessing, model parameter estimation using least squares method, and recursive prediction computation. The model has proven successful in practical applications such as crop yield forecasting and industrial equipment failure rate prediction. When integrated with the AR (AutoRegressive) Prediction Model, which leverages time-series autocorrelation by weighting past observations to forecast future values, the combined system achieves enhanced prediction accuracy. The MATLAB implementation commonly features functions for autocorrelation analysis, order determination via information criteria, and parameter optimization. The synergy between these models allows for comprehensive handling of both trend components (through grey modeling) and stochastic fluctuations (via AR modeling). Key MATLAB implementation aspects include: - Data normalization and sequence transformation for grey modeling - Coefficient calculation using matrix operations for both models - Integration algorithms for weighted combination of predictions - Validation metrics computation (MAPE, RMSE) for performance evaluation This combined forecasting methodology represents a robust analytical tool with extensive applications across multiple disciplines, particularly effective for scenarios with limited historical data and complex pattern recognition requirements.