Using a Grey model optimized by Differential Evolution algorithm to forecast the per capita annual net income of rural households in China

China is a major developing country where farmers account for over 57% of the population. Thus, promoting a rural economy is crucial if the Chinese government is to improve the quality of life of the nation as a whole. To frame scientific and effective rural policy or economic plans, it is useful and necessary for the government to predict the income of rural households. However, making such a prediction is challenging because rural households income is influenced by many factors, such as natural disasters. Based on the Grey Theory and the Differential Evolution (DE) algorithm, this study first developed a high-precision hybrid model, DE–GM(1,1) to forecast the per capita annual net income of rural households in China. By applying the DE algorithm to the optimization of the parameter λ, which was generally set equal to 0.5 in GM(1,1), we obtained more accurate forecasting results. Furthermore, the DE–Rolling–GM(1,1) was constructed by introducing the Rolling Mechanism. By analyzing the historical data of per capita annual net income of rural households in China from 1991 to 2008, we found that DE–Rolling–GM(1,1) can significantly improve the prediction precision when compared to traditional models. ► GM(1,1) is optimized using the DE algorithm and Rolling Mechanism. ► DE–Rolling–GM(1,1) combines Grey Theory, Rolling Mechanism and the DE algorithm. ► DE–Rolling–GM(1,1) is an ideal hybrid model for chaotic forecasting problems.