Application of trembling-hand perfect equilibrium to Nash nonlinear Grey Bernoulli model: an example of BRIC's GDP forecasting

The traditional Grey forecasting model, GM(1,1), is characterized by its linear property. The Nash nonlinear Grey Bernoulli model further increases the forecasting accuracy by considering two governing parameters in the model. Because of the multiple Nash solutions, this study uses trembling-hand perfect equilibrium to refine the NNGBM and then obtains higher forecasting accuracy. This study mathematically proves that the proposed model is feasible and efficient. Finally, NNGBM with trembling-hand perfect equilibrium is used to forecast GDP of four fast-growing countries, Brazil, Russia, India and China, which are abbreviated as BRIC. The results show that BRIC's GDP is keeping on growing.