A novel nonlinear grey Bernoulli model NGBM(1,1,t^p,α) and its application in forecasting the express delivery volume per capita in China

The grey prediction is a common method in the prediction. Studies show that general grey models have high modeling precision when the time sequence varies slowly, but some grey models show low modeling precision for the high-growth sequence. The paper researches the grey modeling for the high-growth sequence using the extended nonlinear grey Bernoulli model NGBM(1,1,t⌃p,α). To improve the nonlinear grey Bernoulli model NGBM(1,1,t⌃p,α)’s prediction precision and make data have better adaptability to the model, the paper makes improvements in the following three aspects: (1) the paper improves the accumulated generating sequence of original time sequence, i.e. making a new transformation of traditional accumulated generating sequence; (2) the paper improves the model’s structure, extends the grey action and builds an extended nonlinear grey Bernoulli model NGBM(1,1,t⌃p,α); (3) the paper improves the model’s background value and uses the value of cubic spline function to approximate the background value. Because the parameters of the new accumulated generating sequence transformed, the nonlinear grey Bernoulli model’s time response equation and the background value are optimized simultaneously, the prediction precision increases greatly. The paper builds an extended nonlinear grey Bernoulli model NGBM(1,1,t⌃2,α) using the method proposed and seven comparison models for China’s express delivery volume per capita. Comparison results show that the extended nonlinear grey Bernoulli model built with the method proposed has high simulation and prediction precision and shows the precision superior to that of seven comparison models.