As the fifth-longest river globally, the Yellow River is of great importance to the world’s ecological protection. Due to its location as an essential ecological barrier and economic zone, it is imperative to balance energy support and ecological management in the basin. In this process, improving energy efficiency is crucial solution. Distinguished into upstream, midstream, and downstream, we measured the trajectory of green total factor energy efficiency over the past fifteen years using the Super-Epsilon-based model. Further, we identified the heterogeneity of energy efficiency within different river basins with the help of kernel density estimation. We used it to analyze the geographical and policy reasons affecting energy efficiency fluctuations. Finally, we constructed high, medium, and low GDP growth scenarios, and used a long short-term memory neural network model to predict energy efficiency forecasts in each scenario. The study results clarified that the overall energy efficiency showed an upward trend since 2013. Among them, the most significant improvement in energy efficiency was observed upstream, while the energy efficiency in the middle and lower stream showed a decreasing trend. Regarding future development trends, an economic growth rate of 6.5% was most favorable for energy efficiency compared to 6% and 7%. This finding reminded us to be alert to the ecological condition of the lower Yellow River basin. In addition, maintaining an appropriate economic growth rate is helpful for the balance between development and ecology.

South Africa’s energy consumption takes up about one-third of that in the whole African continent, ranking the first place in Africa. However, there are few researches on the prediction of energy consumption in South Africa. In this study, based on the data of South Africa’s energy consumption during 1998–2016, Autoregressive Integrated Moving Average (ARIMA) model, nonlinear grey model (NGM) and nonlinear grey model–autoregressive integrated moving average (NGM-ARIMA) model are adopted to predict South Africa’s energy consumption during 2017–2030. After using these NGM, ARIMA and NGM-ARIMA, the mean absolute percent errors (MAPE) are 2.827%, 2.655% and 1.772%, respectively, which indicates that the predicted result has very high reliability. The prediction results show that the energy consumption in South Africa will keep increasing with the growth rate of about 7.49% in the next 14 years. This research result will provide scientific basis for the policy adjustment of energy supply and demand in South Africa and the prediction techniques used in the research will have reference function for the energy consumption study in other African countries.

We have witnessed the rapid growth of coal consumption in past decades. Shandong Province takes 5% of global coal consumption. This paper takes short-term (2016-2020) and long-term (2020-2030) influence into account to predict coal consumption in Shandong Province based on two linear models (ARIMA Model and Metabolism GM (1,1) Model). The MAPE (Mean Absolute Percentage Error) obtained by these two models are respectively 5.6% and 8% and the accuracy obtained by these two prediction models has exceeded 92%, which has reflected the high reliability of the predicted data. The prediction results also show that the coal consumption in Shandong Province will keep increasing with annual growth rate of 1.9% in the next 15 years. The accurate prediction to the coal consumption in Shandong Province will provide scientific basis for the Shandong Province and the country to adjust and formulate the energy supply and demand policies in the future.

Changes in shale gas production directly determine natural gas output in the United States (U.S.), and indirectly impact the global gas market. To better forecast shale gas output, we hybridized a nonlinear model with a linear model to develop a metabolic nonlinear grey model–autoregressive integrated moving average model (or MNGM-ARIMA). The proposed hybrid forecasting technique uses a linear model to correct nonlinear predictions, which effectively integrates the advantages of linear and nonlinear models and mitigates their limitations. Based on existing U.S. monthly shale gas output data, we applied the proposed hybrid technique to forecast U.S. monthly shale gas output. The results show that the proposed MNGM-ARIMA technique can produce a reliable forecasting results, with a mean absolute percent error of 2.396%. Then, using the same set of data, we also ran three other forecasting techniques developed by former researchers: the metabolic grey model (MGM), ARIMA, and non-linear grey model (NGM). The results of the comparison show that the proposed MNGM-ARIMA technique has the smallest mean absolute percent error. This indicates the proposed hybrid technique can produce more accurate forecasting results. We therefore conclude that the proposed MNGM-ARIMA technique can service us better forecasting shale gas output, as well as other fuels output.

South Africa’s coal consumption accounts for 69.6% of the total energy consumption of South Africa, and this represents more than 88% of African coal consumption, taking the first place in Africa. Thus, predicting the coal demand is necessary, in order to ensure the supply and demand balance of energy, reduce carbon emissions and promote a sustainable development of economy and society. In this study, the linear (Metabolic Grey Model), nonlinear (Non-linear Grey Model), and combined (Metabolic Grey Model-Autoregressive Integrated Moving Average Model) models have been applied to forecast South Africa’s coal consumption for the period of 2017–2030, based on the coal consumption in 2000–2016. The mean absolute percentage errors of the three models are respectively 4.9%, 3.8%, and 3.4%. The forecasting results indicate that the future coal consumption of South Africa appears a downward trend in 2017–2030, dropping by 1.9% per year. Analysis results can provide the data support for the formulation of carbon emission and energy policy.