An approach to increase prediction precision of GM(1,1) model based on optimization of the initial condition

Abstract

We propose a novel approach to improve prediction accuracy of GM(1,1) model through optimization of the initial condition in this paper. The new initial condition is comprised 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 can actually find that the newly modified GM(1,1) model is an extension of the original GM(1,1) model and another modified model which takes the last item in the generated sequence as the initial condition when weighted coefficients takes distinctly specific values. 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 GM(1,1) model presented in this paper can obtain a better prediction performance than that from the original GM(1,1) model.