Parameter estimation of modified gray model GM (1, N) and model application

Abstract

The GM (1, N) model is an important prediction model among gray models, but the conventional GM (1, N) model shows big errors sometimes mainly due to the structural inconsistency between the gray differential equation for parameter estimation and the whitening equation for prediction. The paper derives the modified model of conventional gray differential equation based on the whitening equation, and the gray differential equation obtained in this way has the structure basically consistent with the structure of whitening equation. The paper estimates parameters with the gray differential equation of modified GM (1, N) model and gives three parameter estimation methods with different background values. The time response equation for conventional GM (1, N) model generally has no analytical solution, but the paper gives a specific solving method for the time response equation of modified model. The example proves that the modified GM (1, N) model given and the models built with the methods proposed improve the simulation and prediction accuracy significantly compared with the conventional model.

Keywords:

• Gray differential equation
• Gray prediction
• Parameter estimation
• Time response equation
• Whitening equation

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F99
• 93A30

Additional information

Funding

The authors are grateful for the National Natural Science Foundation of China (11401418).