A novel elastic net-based NGBMC(1,n) model with multi-objective optimization for nonlinear time series forecasting

Abstract

Nonlinear grey Bernoulli multivariate model NGBMC (1, n) is known as a novel forecasting model for nonlinear time series with small samples. However, ill-posed problem would make it less efficient and even cause large errors. In order to improve its generality, a hybrid method combining Elastic Net and multi-objective optimization is introduced in this work. This method effectively solves the essential defect of the ill-posed problem of the NGBMC (1, n) model, making the NGBMC (1, n) model more stable, more reliable, and more interpretable. The parameter identification of the new model uses the alternating direction method of multipliers, and the nonlinear parameter of the model and the regularization parameter of Elastic Net regression are optimized by the multi-objective grey wolf optimizer (MOGWO). Eight numerical cases all show that the use of the Elastic Net regularization method and multi-objective optimization technology can significantly improve the prediction accuracy of the NGBMC (1, n) model for future data. In addition, the hybrid method combing the regularization and optimization strategies proposed in this paper is a general framework for the grey prediction models, which has a high potential in improving the other grey models.