A novel time-delay neural grey model and its applications

Grey system theory uses differential equations to model small sample time series to predict the short-term development law of things in the future. Since the most classical GM(1, 1) model was proposed, many scholars have improved it and derived various grey models that can predict linear or nonlinear time series. However, the existing grey models are still not accurate enough for constructing background values and parameter estimation methods. In order to improve the accuracy and applicability of the grey model, a novel neural grey model with accumulated time delays is proposed in this paper. In this model, the whitening equation of the grey model is constructed by combining the long short-term memory network to add time-delay variables to the original grey model. Second, the neural ordinary differential equation (NODE) is used to train the model to determine the time delays, the time-delay weights, and the model parameters to obtain better predictions. Finally, the Euler method is used to get the final prediction series. The new model’s performance is tested through experiments on energy consumption and CO2 emissions prediction. The results were compared with some grey models, support vector regression (SVR), and autoregressive integrated moving average models (ARIMA). It can be concluded that the new model has better generalization performance and higher prediction accuracy than the selected comparative models.