Makbul Muksar, Syafi'udin Zuhri
Forecasting can be said as a way or technique to estimate a value in the future by paying attention and considering past data and present data. One of the forecasts used is the Gray Forecasting model, namely GM(1, 1) and GM(2, 1). In this study, the GM(3, 1) forecasting model will be developed as the development of the GM(1, 1) and GM(2, 1) models. The GM(2, 1) model is an improvement from the GM(1, 1) model, especially for data that has a large difference in each period. The model uses an ordinary differential equation of order 1 (one) for GM(1, 1), of order 2 (two) for GM(2, 1), with each model using 1 (one) variable. The research conducted by Guo-Dong Li obtained a relatively large error using GM(2, 1) for fluctuating data so that in this study the development and modification of the GM(2, 1) model was carried out so that the error value was lower than before. The purpose of the study was to develop The GM(3, 1) model developed from of GM(1, 1) and GM(2, 1) model by using differential equations of order 3 (three) and still using 1 (one) variable. Furthermore, to test the accuracy of the GM(3, 1) model, three types of data will be used, namely increasing monotonic data, decreasing monotonic data, and fluctuating data. From the simulation results, only accurate fluctuating data is obtained for the GM(3, 1) model compared to the GM(2, 1) model and the GM(1, 1) model. By using MAPE to determine the error, the error for data that fluctuates in the GM(3.1) model is 3.909611772% which is better than the error in the GM(l.l) model, which is 6.051558% and the GM model error(2.1) of 56.03034%). Furthermore, because the error of the GM(2, 1) model > 50%>, it is categorized as a weak and inaccurate forecast, while the error for the GM(1, 1) and GM(3, 1) models which is less than 10%> are categorized as forecasting with a high level of accuracy with the best accuracy is the GM(3, 1) model. © 2022 American Institute of Physics Inc.. All rights reserved.
Department of Mathematics, State University of Malang, Jalan Semarang 5, East Java, Malang, 65145, Indonesia