A Fractional Order Opposite-direction Accumulative Grey Prediction Model with Time-power

To improve the forecasting performance of grey model based on monotonically decreasing sequence, the 1-order opposite-direction accumulative grey model with time power (abbreviated as GOM(1,1,t(alpha))) and fractional order opposite-direction accumulative grey model with time-power (abbreviated as GOM(r) (1, 1,t(alpha))) are proposed respectively on the basis of previous research. The time response functions of the two models are given by using the compound 3/8 Simpson integral formula. Considering modelling error and restoring error, it is proved that there exists a fractional order in the interval [0,3) such that GOM(r) (1,1,t(alpha)) model can achieve the best fitting performance when the other parameters are fixed values. Finally, some examples are given to test the performance of the proposed models. The results show that the proposed models exhibit higher simulative and predictive precision compared with the traditional GOM(1,1) model.