Improving GM(1,1) Model Performance Accuracy Based on the Combination of Optimized Initial and Background Values in Time Series Forecasting

The term grey forecasting model has been comprehensively utilized in numerous research arenas and discovered valid outcomes. Nevertheless, the model possesses certain possible problems that necessitate improvement. It has been proven that, part of the foremost issues distressing the prediction accurateness of the model are initial and background values. Henceforth, a new modified GM(1,1) model through the combination of optimized initial value and background value has been recommended in this study. The new initial value encompasses the median value of a sequence that has been generated using the first-order accumulative generating operation on the raw data sequence while the number of observations is odd or even. Meanwhile, in the standard model GM(1,1), the background value is rebuilt using an integral term to rectify the error term caused by the background value computation. An empirical study of real data was performed to validate the proposed model’s prediction accuracy in this article. The real datasets were analyzed using R Code. The obtained findings showed that the modified model GM(1,1) has lower error as well as higher accuracy, which enriches grey model optimization theory and broadens the field of grey model implementation in time series forecasting.