Application of improved seasonal GM(1,1) model based on HP filter for runoff prediction in Xiangjiang River

Runoff forecasting is essential for the reasonable use of regional water resources, flood prevention, and mitigation, as well as the development of ecological civilization. Runoff is influenced by the intersection of many factors, and the change process is extremely complex, showing significant stochasticity, nonlinearity, and heterogeneity, making traditional prediction models less adaptable. The Hodrick-Prescott filter (HP filter) is a well-established signal separation method. The traditional GM(1,1) model is capable of portraying the growth trend of the time series but cannot capture the periodic characteristics of the time series. Therefore, a novel coupled prediction model-HPF-GM(1,1) model is proposed in this study and applied to the runoff prediction of the Zhuzhou section of Xiangjiang River in Hunan Province. This model enables to separate seasonal factors from non-seasonal factors in the runoff time series, and introduce seasonal factors based on the traditional GM(1,1) model, which solves the challenge that the traditional GM(1,1) model is unable to predict seasonal time series. The results show that the HPF-GM(1,1) model has a mean relative error of 4.82%, a root mean square error of 7.44, and a Nash efficiency coefficient of 0.93, which is better than the traditional GM(1,1) model, the DGGM(1,1) model and the SGM(1,1) model of prediction accuracy. Obviously, the HP filter provides a new approach to data pre-processing of runoff series and the proposed HPF-GM(1,1)-coupled model extends new ideas for nonlinear runoff prediction.