Forecasting the output of shale gas in China using an unbiased grey model and weakening buffer operator

China has the richest shale gas resources worldwide. However, the exploitation of shale gas in China is very recent, and historical data on the output of shale gas are extremely limited (only five data points exist). Consequently, common mathematical models designed for use with big data cannot be used to forecast the shale gas output in China. Grey models can be constructed by using small samples; however, traditional grey models have the drawback of 'misplaced replacement' during the conversion from a difference equation to a differential equation. Thus, a new unbiased grey prediction model called UGM(1,1) is proposed and optimised in this study. A grey weakening buffer operator was employed to pre-process the primary data on Chinese shale gas output to eliminate the contradiction between the prediction results of models and the conclusions of qualitative analysis. The UGM(1,1) model was then used to simulate the output of shale gas in China, and found to outperform other grey models. Finally, we forecasted the output of shale gas in China from 2017 to 2025, and analysed the rationality of the prediction data. The study findings will be of important reference value for use by the Chinese government to formulate energy policies.