The Optimization of Grey Verhulst Model and Its Application

Grey theory is an approach that can be used to construct a model with limited samples to provide better forecasting advantages for short-term problems. The Grey Verhulst Model is a typical grey forecasting model in grey theory. As the background value is an important factor affecting the precision of the grey system model, the optimization of background value in grey Verhulst model is studied in this paper. First, the numerical relationship between background value and development coefficient is discussed; then, after transformation of the grey Verhulst model, new parameters are evaluated by the least square method, and the estimated values of original parameters are calculated by equations. The new background value satisfies the criteria of unbiasedness and least error. In the end, the proportion of non-agricultural population in Shanghai during the period of 2003-2012 is simulated and forecasted by three grey Verhulst models. The empirical results show the precision of simulation and prediction of the new optimized model is obviously higher, and the efficiency and feasibility of the optimized model are validated. This paper contributes significantly to improve grey forecasting theory, and proposes a modified Grey Verhulst model.