Forecasting Taiwan’s major stock indices by the Nash nonlinear grey Bernoulli model

The mathematics of traditional grey model is not only easy to understand but also simple to calculate. But, the linear nature of its original model results in the inability to forecast the drastically changed data of which essence is in nonlinear. For this reason, this study investigates cases using nonlinear grey Bernoulli model (NGBM) to demonstrate its ability in forecasting nonlinear data. The NGBM is a nonlinear differential equation with power n. The power n is determined by a simple computer iterative program, which calculates the minimum average relative percentage error of the forecast model. Furthermore, the authors improve NGBM by Nash equilibrium concept. The Nash NGBM (NNGBM) contains two parameters, the power n and the background value p, which increase the adjustability of NGBM model. This newly proposed model could enhance the modeling precision furthermore. In order to validate the feasibility of the NNGBM concept, the NNGBM is applied to forecast the monthly Taiwan stock indices for 3rd quarter of 2008. The forecasting results show: (1) the NNGBM actually improve the forecasting precision, (2) the Taiwan’s stock markets tend to be a bear market from July 2007 to September 2008, and the whole investing environments will prevail with collapsing financial prices, pessimism and economic slowdown.