A New Background Value Improvement of Fractional Order Accumulated FAGM(1,1) Model and Its Application

The prediction accuracy of the fractional FAGM(1,1) model mainly depends on the calculation of the background value. To improve the prediction accuracy of the FAGM(1,1) model, a new background value calculation method is proposed. By analyzing the cause of the background value error, considering the regularity of the fractional-order accumulation sequence with non-homogeneous exponential growth, the non-homogeneous exponential curve is used to fit the fractional-order accumulation sequence, combined with the integral theory, to accumulate the actual sequence on the interval. The result of the integration is used as a new background value. The example shows that using the new background value calculation method combined with the Genetic Algorithm to find the optimal order, the fitting and prediction accuracy of the fractional FAGM(1,1) model is obviously improved, and the background value has the characteristics of simple calculation and strong practicability.