An optimized nonlinear grey Bernoulli model and its applications

• An optimized NGBM(1,1) is proposed and proved to be efficient.
• Initial condition, power exponent and background value are optimized together.
• A simultaneous optimization method is adopted to calculate the parameters.

Nonlinear grey Bernoulli model (NGBM) is a recently developed grey forecasting model, and this investigation will propose an optimized NGBM(1,1) (ONGBM). ONGBM takes the n-th component of 1-AGO series as initial condition, which is also optimized with a boundary value correction method. Meanwhile, ONGBM adopts a simultaneous optimization approach to calculate the unknown parameters aiming at achieving the minimization of simulated average relative error. One actual forecasting example of foreign exchange rates is chosen for practical test of ONGBM, and the results are encouraging. Subsequently, ONGBM is applied to forecast the traffic flow with nonlinear small sample characteristics. The simulation results demonstrate that ONGBM is feasible and efficient, and it can improve the prediction accuracy and adaptability.