Using fractional order accumulation to reduce errors from inverse accumulated generating operator of grey model

To smooth the randomness, a grey forecasting model is formulated using the data of accumulating generation operator (AGO) rather than original data. Then the inverse accumulating generation operator (IAGO) is applied to find the predicted values of original data. It is proved that the errors from IAGO are affected by the order number of AGO. To achieve an accurate prediction, GM(2,1), which stands for one-variable and second-order differential equation, has been improved by means of fractional order AGO. Finally, four real data sets are imported for comparing the performance of the developed GM(2,1) with several other grey models, such as traditional GM(2,1) and GM(1,1). The simulation results show that optimized GM(2,1) has higher performances not only on model fitting but also on forecasting.