Nonlinear grey Bernoulli model based on Fourier transformation and its application in forecasting the electricity consumption in Vietnam

Abstract

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 scenarios. In order to expand the field of application and to improve the predictive quality of the NGBM (1, 1) model, this paper proposes an effective model (named 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 use a Fourier series to filter out and to select the low-frequency error values. To test the superior ability of the proposed model, two numerical data sets were used. One is the historical data of annual water consumption in Wuhan from 2005 to 2012 in He et al. ’s paper, and the other is example data from Wang et al. ’s paper. The forecasted results prove that the performance of the Fourier-NGBM (1, 1) model is better than three other forecasting models, namely GM (1, 1), NGBM (1, 1) and the improved Grey Regression model. Furthermore, this study also applied the proposed model to forecast the electricity consumption in Vietnam up to the year 2020. The empirical results can offer valuable insights and provide basic information for model building to develop future policies regarding electrical industry management. In subsequent research, more methodologies can be used to reduce the residual error of the 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 fluctuating data and uncertain information.