Point and Interval Forecasting of Groundwater Depth Using Nonlinear Models

This study focuses on the development of a new model that can be used not only to forecast the groundwater depth but also to quantify the uncertainty of forecasts. Therefore, we built a hybrid of Self-Exciting Threshold Autoregressive-Generalized Autoregressive Conditional Heteroscedasticity model, namely SETAR-GARCH model to obtain point and interval forecasts of groundwater depth. In addition, single SETAR model and a hybrid of SETAR and Kernel Density Estimation model, referred as SETAR-KDE, were compared. Two average monthly groundwater depth of Xi'an and Baoji cities in Shaanxi, China, were used to evaluate the models. The study results demonstrate that the SETAR-GARCH model achieves satisfactory point and interval forecasting performance and reduces the uncertainty of interval forecasting. Furthermore, we found and proved a significant finding that the GARCH model does not have any influence on the point forecasting, but it can achieve superior performance of interval forecasting by combined with SETAR model. This study may provide a new idea for nonstationary and nonlinear groundwater depth prediction and further provide a reference for the design and management of water systems in the changing environment.