Smoothness Optimization of the Original Sequence for Grey Model GM(1,1)

This article explores smoothness optimization techniques for the original sequence in Grey Model GM(1,1). First, we need to understand the fundamentals of GM(1,1) – a widely used model for time series analysis that employs grey prediction methods to forecast future trends. To enhance the accuracy of the GM(1,1) model, smoothness optimization of the original sequence requires implementing mathematical methods that improve data smoothness, thereby increasing prediction reliability. These mathematical approaches include: - Weighted moving averages (implemented through convolution operations with customized weight matrices) - Accumulated generating operation (AGO) sequences, which transform the original data through cumulative summation - Exponential smoothing techniques using decay factors to prioritize recent observations In code implementation, these methods typically involve creating sliding window algorithms for moving averages, writing cumulative sum functions for AGO transformation, and applying exponential weighting formulas for smoothing. Through these optimization techniques, we can develop more accurate GM(1,1) models that provide precise future trend predictions. Therefore, when conducting time series analysis, smoothness optimization of raw data represents a crucial preprocessing step that significantly impacts model performance.