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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.

The precise prediction of foreign exchange rate is very important for international traders and investors. This study adopts nonlinear grey Bernoulli model (NGBM) and Nash NGBM (NNGBM) to predict the currency exchange rate of Taiwan's two top trading partners, America and China. The simulation results show that Taiwan's currency will appreciate against USD and CNY from the fourth quarter of 2015 to the second quarter of 2016. The conclusions can act as reference for international traders and investors.

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