An unbiased non-homogeneous grey forecasting model and its applications

In response to the limitations of the traditional grey forecasting model in terms of structure and parameters, an unbiased non-homogeneous grey forecasting model containing a nonlinear time term is proposed. First, the background value is improved based on the integral median theorem, which in turn gives a new unbiased parameter estimation method. Second, the optimization effect of the model is further enhanced by better selection of initial value through relative error sum of squares minimization. It not only has the number multiplication transformation consistency, but also can be compatible with many existing grey forecasting models by adjusting its own structural parameters. Third, the unbiasedness and effectiveness of this model are verified with the help of matrix theory and three practical cases, respectively, and the results show that its performance is more advantageous compared with other grey models as well as various time series forecasting models. Finally, the model is applied to the forecasts for consumer expenditure and food production, with in-sample errors of 0.722% and 0.471%, and out-of-sample errors of 1.341% and 0.827%, respectively. Forecasts show that the per capita consumption expenditure of rural residents in Sichuan Province will reach about 23,000 yuan, and grain production in Jiangsu Province will reach about 39.9 million tons in 2027.