A 'basic form'-focused modeling and a modified parameter estimation technique for grey prediction models

Grey modeling is an alternative approach to time series forecasting with growing popularity. There is no theoretical limitation for grey prediction models to adapt to almost every process by taking the appropriate order. However, deficiencies of traditional higher-order models have made researchers overlook such flexibility and make use of first-order models by default. In order to bridge the mentioned gap, this paper makes two contributions. First, a novel discrete modeling is developed with the basic form equation at its heart, which reconciles estimation and prediction processes. Second, the traditional least-squares estimation technique is modified by shifting the focus from nominal parameters to parameters practically employed in the prediction process. The new approach named ‘Basic Form’-focused Grey Model (BFGM) is applied to first-order, second-order, and Verhulst grey models. Then, it is validated through comparing its performance with the traditional approach. Results show that in most cases BFGM makes considerable improvements in simulation and prediction accuracy, while it has reasonable computational complexity. Improvements are especially dramatic when BFGM is applied to GM (2, 1). The resultant BFGM (2, 1) is superior in simulation and short-term prediction and, therefore, can be regarded as the basis for developing efficient higher-order grey formulations.