The optimized GPM(1,1) for forecasting small sample oscillating series

The purpose of this paper is to provide a modeling approach using grey power model with first‐order one‐variable (abbreviated as GPM(1,1)) for forecasting small sample oscillating series.

An optimization method is used to determine the initial value in GPM(1,1) model, and furthermore, the power value in the model is optimized by utilizing a non‐linear programming model. An operations research software LINGO is employed to solve the non‐linear optimization model.

The results show that the optimized GPM(1,1) model can flexibly adjust the parameters to make the forecasting results more in line with the actual data; therefore, for a given small sample oscillating series, if an appropriate way to find the optimal parameters is taken, accurate predictions should be obtained.

The modeling approach proposed in the paper can be used to forecast new product sales, new industry development trend, equipment remaining life, disaster emergency material demand, etc.

The paper extends the application range of the grey model for forecasting small sample oscillating series by using grey power model GPM(1,1).