Using Fourier Series to Improve the Prediction Accuracy of Nonlinear Grey Bernoulli Model

摘要

In recent decades, the Nonlinear Grey Bernoulli model "NGBM (1, 1)" has been applied in various fields and achieved positive results. However, its prediction results may be inaccurate in different scenario. In order to expand the field of application and to improve the predict quality of NGBM (1,1) model, this paper proposes an effective model (named as Fourier-NGBM (1, 1)). This model includes two main stages; first, we get the error values based on the actual data and predicted value of NGBM (1, 1). Then, we used Fourier series to filter out and to select the low- frequency their error values. To test the superior ability of the proposed model, the historical data of annual water consumption in Wuhan from 2005 to 2012 in He et al.' paper is used. Forecasted results proved that the performance of Fourier-NGBM (1, 1) model is better than three forecasting models which are GM (1, 1), NGBM (1, 1) and improved Grey-Regression model. In subsequent research, more methodologies can be used to reduce the residual error of NGBM (1, 1) model, such as Markov chain or different kinds of Fourier functions. Additionally, the proposed model can be applied in different industries with the fluctuation data and uncertain information.