An improved GM(1,1) model based on weighted MSE and optimal weighted background value and its application

Area of Science:

• * Mathematical modeling and forecasting
• * Time series analysis and prediction

Background:

• * The GM(1,1) model is popular for its minimal data requirements, low computational complexity, and lack of statistical assumptions.
• * A key limitation of existing GM(1,1) models is their insufficient prediction accuracy, despite satisfactory fitting accuracy.

Purpose of the Study:

• * To develop an improved GM(1,1) model with superior prediction accuracy.
• * To address the common drawback of poor predictive performance in conventional GM(1,1) models.

Main Methods:

• * Proposed an optimized GM(1,1) model incorporating weighted mean squared error (MSE) and an optimal weighted background value.
• * Developed the OB-WMSE-GM(1,1) model to enhance predictive capabilities.

Main Results:

• * The OB-WMSE-GM(1,1) model demonstrated significantly lower fitting and prediction errors (MSE, WMSE, MAPE) compared to the typical GM(1,1) model in simulation and real-world examples (LCD TV production, crude oil processing).
• * For instance, in the exponential function simulation, the proposed model's predicting MSE was 0.015485, vastly outperforming the typical GM(1,1)'s 1.144524.
• * Similar improvements were observed in annual LCD TV output and crude oil processing volume predictions.

Conclusions:

• * The proposed OB-WMSE-GM(1,1) model offers a substantial improvement in prediction accuracy over traditional GM(1,1) models.
• * Further performance enhancements are possible by integrating the proposed method with techniques like residual modeling and optimized initial conditions.