Grey power models based on optimization of initial condition and model parameters

We propose a novel approach to improve prediction accuracy of grey power models including GM(1,1) and grey Verhulst model through optimization of the initial condition and model parameters in this paper. And we propose a modified grey Verhulst model. The new initial condition consists of the first item and the last item of a sequence generated from applying the first-order accumulative generation operator on the sequence of raw data. Weighted coefficients of the first item and the last item in the combination as the initial condition are derived from a method of minimizing error summation of square. We shows that the newly modified grey power model is an extension of the previous optimized GM(1,1) models and grey Verhulst models. The new optimized initial condition can express the principle of new information priority emphasized on in grey systems theory fully. The result of a numerical example indicates that the modified grey model presented in this paper can obtain a better prediction performance than that from the original grey model.