Ordinary Least Squares based on Fourier Series Residuals for fitting the Modified Exponential Growth Model

Abstract

Abstract It is well-known that grey system theory was put forward in the statistical literature to overcome the problem of partially unknown parameters, therefore it is given the attention of the researchers in many scientific areas. Therefore, many methods have been presented in which the grey system is combined with the Fourier series and others for more accurate prediction. This paper presents a methodology to modify the method of least squares based on Fourier series residuals that are computed by using grey system theory. The objective of this methodology is to improve the estimates of a modified exponential growth model. The performance of the proposed method by using simulation is compared with two famous methods and the results show our proposed method outperforms more than others and it is highly efficient and reliable. On the practical, the new method was used to predict the price of a barrel of crude oil for the OPEC basket for the period from Jul 2019 to Dec 2019, and It can be seen that OPEC basket prices will decline in the end of 2019.