Grey Prediction and its MATLAB Implementation

In this article, we will explore the concept of grey prediction and demonstrate its implementation using MATLAB. Grey prediction is a mathematical model-based forecasting method widely applied across various domains including finance, economics, environmental science, and healthcare. The core principle involves transforming uncertain systems into deterministic systems through mathematical modeling for predictive analysis. When implementing grey prediction in MATLAB, the process involves several key computational steps: - Data preprocessing through cumulative generation operations to strengthen data regularity - Construction of GM(1,1) model using differential equations with parameter estimation via least squares method - Precision verification through posterior variance tests and residual analysis - Predictive computation using time-response functions with inverse cumulative reduction This article provides detailed MATLAB implementation guidelines, including: 1. Code structure for data normalization and sequence transformation 2. Algorithm implementation for background value coefficients and development coefficients 3. Functions for model accuracy evaluation (mean absolute percentage error calculation) 4. Case studies demonstrating practical applications with complete code examples Through this tutorial, readers will gain comprehensive understanding of grey prediction fundamentals and develop practical MATLAB programming skills for time-series forecasting, enhancing their technical capabilities in predictive modeling applications.