A novel fractional neural grey system model with discrete q-derivative

Abstract

The challenge of predicting time series with limited data has evolved over time due to nonlinearity, complexity, and limited information. It can be perceived as a mapping of dynamical systems in one-dimensional space. This article proposes a neural grey system to tackle this challenge. The system enhances its ability to fit nonlinearity by employing polynomials, captures complexity through a fractional-order cumulant operator, and resolves information-poor uncertainty by utilizing grey system modeling techniques. The model effectively integrates research findings from neural computing, uncertainty theory, and complexity theory at a theoretical level. It accurately describes dynamic processes of complex systems. Additionally, we have reduced the complexity of calculations in the algorithm design. We selected a dataset of total retail sales of consumer goods to test the model’s validity and applicability. Our experiments demonstrate that the newly proposed grey forecasting model can effectively forecast time series with small samples, offering good forecasting outcomes and generalization ability.