The improved grey model based on particle swarm optimization algorithm for time series prediction.

Grey theory is one of the most common methods for solving uncertain problems using limited data and poor information, due to its high performance in time series prediction. However, the inappropriate background value and initial value are the main factors affecting prediction accuracy of the Grey Model GM(1,1). An improved grey model based on particle swarm optimization algorithm named PGM(1,1) is proposed for time series prediction in this paper. The development coefficient of the grey model is calculated by PGM(1,1) based on particle swarm optimization, targeting at minimizing the average relative errors between the restored value and real value of the model to avoid the problem caused by background value optimization. In addition, the initial value of the Grey Model GM(1,1) is optimized and a sliding window is introduced to improve both precision and adaptability. Finally, three data sets, featuring increasing trend, decreasing trend, and wide fluctuations, are used in the experiments, showing that the proposed method achieves better prediction accuracy.