Two novel nonlinear multivariate grey models with kernel learning for small-sample time series prediction.

Area of Science:

• Time Series Analysis
• Forecasting Models
• Computational Intelligence

Background:

• Grey forecasting models are crucial for small-sample time series prediction.
• Existing methods have specialized applications based on data properties.
• There is a need for generalized nonlinear multivariable grey models with improved compatibility and performance.

Purpose of the Study:

• To develop a generalized nonlinear multivariable grey model (NGM(1,N)) for enhanced time series prediction.
• To improve compatibility and generalization performance of grey forecasting models.
• To explore nonlinearization of traditional GM(1,N) models.

Main Methods:

• Nonlinearization of the traditional GM(1,N) model to create NGM(1,N).
• Parameter estimation using Lagrange multipliers and standard dualization methods.
• Incorporation of kernel functions to reduce computational complexity of nonlinear functions.

Main Results:

• The proposed NGM(1,N) model demonstrates improved generalization performance.
• The Lagrange multiplier method converts the optimization problem into a solvable linear system.
• Kernel functions effectively handle nonlinearities, reducing computational load.

Conclusions:

• The developed nonlinear multivariable grey model (NGM(1,N)) offers superior generalization capabilities.
• Duality theory and kernel learning provide a robust framework for future multivariate grey model research.
• The LDNGM(1,N) model outperforms existing multivariate grey models in numerical examples.