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

The purpose of this paper is to propose a novel approach to improve prediction accuracy of grey power models including GM(1, 1) and grey Verhulst model.

The modified new models are proposed by optimizing the initial condition and model parameters. The new initial condition consists of the first item and the last item of a sequence generated by applying the first-order accumulative generation operator on the sequence of raw data.

It is shown that the newly modified grey power model is an extension of the previous optimized GM(1, 1) and grey Verhulst model. And the optimized initial condition reflected the principle of new information priority.

The result of a numerical example indicates that the modified grey model presented in this paper with better prediction performance.

The new initial condition are derived by weighted combination of the first item and the last item. The coefficients of weight obtained by the least square method.