Probabilistic accumulation grey forecasting model and its properties

In grey system theory, the performance of an established grey forecasting model largely depends on how efficiently the grey information can be measured from data. Most existing grey forecasting models use grey accumulating generators to obtain grey information. However, not all grey information helps improve the performance of grey forecasting models. Consequently, simple accumulation leads to the accumulation of error from invalid grey information, which deteriorates the model performance. To address this issue, valid and invalid grey information were defined in this study according their contributions to the model performance. Further, it was proposed to use a Bernoulli distribution to simulate the distribution of valid/invalid grey information. Based on that probability, a probabilistic accumulation operator was designed to compute grey information, and this grey information was utilized to establish a probabilistic accumulation operator-based grey forecasting model (PGM(1,1)). PGM(1,1) is advanced in terms of forecasting because it is not negatively affected by invalid grey information. PGM(1,1) was tested on five public datasets and compared to other grey models as well as a wide range of other forecasting models, achieving state-of-the-art performance. In addition, a comprehensive analysis was conducted to demonstrate how the forecasting performance benefits from identifying valid/invalid grey information in PGM(1,1).