Narrow Results

This study presents a novel fractional order grey model FGM ($\alpha$,1) obtained by extending the grey model (GM (1,1)). For this, we generalize the whitenization first-order differential equation to fractional order by using the Caputo fractional derivative of order $\alpha$. A real-world case study, scrutinize the economic growth influence on environmental degradation in Turkey, is performed to evaluate the significance of the projected model FGM ($\alpha$,1) in contrast to the current classical GM. We apply autoregressive distributed lags bounds testing co-integration approach to empirically examine the long-run and short-run relation among economic growth, agriculture, forestry and fishing (AFF), electricity utilization and CO₂ emissions. Using the new fractional order model, all the variables are forecasted in the forthcoming years until 2030. Findings disclose that electricity utilization and economic growth (GDP) accelerate emission of CO₂ though in the long run agriculture, forestry, and fishing reduce the environmental pollution in Turkey.

According to the principle of minimum information, new information priority, and difference information, most existing grey forecast models and their improvement are inconsistent with the grey theory. Therefore, a novel discrete multivariable grey model with unequal fractional-order accumulation is proposed. To improve the accuracy and stability of the model, an optimization algorithm for unequal fractional-order is proposed. The proposed model and algorithm are evaluated with four actual cases. The results show that the novel model has better performance and the proposed unequal fractional-order accumulation operator is better than other existing accumulation operators. Considering the energy consumption, the carbon dioxide emissions in the USA have been forecasted to decrease but remain at a high level by using the novel discrete multivariable grey model. Reducing energy consumption is conducive to reducing carbon dioxide emissions.

Accidents involving heavy metal pollution of water and the environment cause huge casualties and loss of property, making the monitoring of heavy metal pollution of great importance. In order to overcome the disadvantages of the traditional model algorithm, such as low predictive accuracy and poor fusion ability, a new combined forecasting model was developed based on the autoregressive integrated moving average model and grey theory. The autoregressive integrated moving average model time series forecasting methods were used to make a preliminary forecast for heavy metal historical data. Then a non-interval GM(1,1) model was built. The model residual of initial forecasts were put as the input of GM(1,1) to be modified. The non-interval GM(1,1) model is established regarding the residual value of the ARIMA. Finally, the initial forecasts of ARIMA model and the residual prediction value of GM(1, 1) fusion and combination forecast GM-ARIMA model were constructed. The heavy metals monitoring data of a river in Hebei province in 1978–2007 were taken as the sample to be analyzed. The predictive results of the autoregressive integrated moving average model, GM(1,1) model and the GM-ARIMA model are compared. The results show that the GM-ARIMA model has better predictive performance and fusion ability.