Nonlinear grey multivariable prediction model with time-varying delay function and its application

Purpose Accurate prediction serves as a critical foundation for formulating and optimizing industrial development strategies, particularly in projecting the output of the high-tech industry through a scientific approach. Design/methodology/approach A novel nonlinear time-varying delay grey multivariable model (NTVDGM(1,N)) is designed in this work. First, we propose a new time-varying delay function, which can overcome the constraint of a fixed time delay in the existing grey time-delay models. On this basis, a new cumulative time-delay function combined with the Gamma function is constructed, indicating a decreasing trend and an inverted U-shaped trend. Then, the power parameter is designed to express the nonlinear relationship between the inputs and outputs, and the Grey Wolf Optimization (GWO) algorithm is selected to determine the hyperparameter. Findings Simulations validate the robustness and stability of the (NTVDGM(1,N)) model, demonstrating that the proposed model possesses superior forecasting accuracy. Practical implications The proposed model is applied to project the output of the high-tech industry in Guangdong province, the grey and non-grey prediction models are selected for comparison to the new model, and the results show that the (NTVDGM(1,N)) model achieves a satisfactory prediction accuracy in forecasting the high-tech industry's output. Originality/value This work proposes a novel nonlinear time-varying delay grey multivariable model with a cumulative function and variable time-delay parameters to capture the dynamic time-delay effect.