ABGM(1,1): A Joint Optimization GM(1,1) Model Based on Background Values and Initial Conditions

The classical GM(1,1) model is suitable for making accurate forecasts of small samples. However, the accuracy of model prediction result is affected by multiple factors, such as the calculation method of background value and the construction of initial conditions, etc. Most optimized models focus on single influence factor. This study proposes a joint optimization method about background value and initial condition, which includes a logical, calculating formula of background value based on Aitken interpolation and a relatively ingenious algorithm of the initial condition by adding an arbitrary normal number. Furthermore, the new model is used to predict three different types of data sequences. High precision is found by comparing prediction data.