Forecasting CO2 Emissions Using a Novel Conformable Fractional Order Discrete Grey Model

Abstract

Accurate and scientific forecasting of carbon dioxide emissions will help make better industrial carbon emission planning so as to promote low-carbon industrial development and achieve sustainable economic growth. For depressing the disturbance of various elements, grey system-based models play an important role in forecasting science. In this paper, we extend the cumulative order from integer order to fractional order based on the discrete gray model, which we call CFDGM (1,1). After introducing the free quantity of the model order, the accuracy of the prevenient grey-based models can be further enhanced. We selected the data for carbon dioxide production by Germany, Japan, and Thailand for modeling. To obtain the optimal order of our grey model, we selected four optimizers to search for the order. The results show that although the search history of the four types of optimizers is different, the search results are the same, which proves that the four types of optimizers are stable and reliable, and the order for which we searched is reliable. By substituting the optimal order into CFDGM (1,1), we obtained the fitting and prediction error of the proposed model. The final results show that a satisfactory fitting effect and forecasting effect is obtained by our proposed model.