Forecasting Nonlinear Time Series Using an Adaptive Nonlinear Grey Bernoulli Model: Cases of Energy Consumption

It is appropriate to apply the forecasting model based on grey theory when the relevant data are hard to come by, non-linear and non-normal. An extended version of the NGBM(1,1) is addressed, which simultaneously takes adjustable hyper-parameters such as power exponent, smoothing factor of background value, selection of initial conditions and scaling factor of residual modification into consideration. We then apply the procedures of hyper-parameter optimization and hyper-parameter screening using the genetic algorithm (GA) and the 2(k) factorial design so as to alleviate the problems of manual selection of hyper-parameters and over-fitting, respectively. The resulting model is called an adaptive NGBM(1,1) which does not deviate from the simple ideas of grey theory. In this study, a preliminary comparative analysis is conducted in two benchmark sequences and two real-world sequences for China's energy consumption. The results of this analysis are used to simulate fluctuating and smooth data conditions for evaluation purposes. The experimental results suggest that the high-precision adaptive NGBM(1,1) can potentially improve the effectiveness of decision making.