DAR-type model based on “long memory-threshold” structure: a competitor for daily streamflow prediction under changing environment

The non-stationarity and non-linearity of streamflow have increased with changes of the environment, challenging accurate streamflow prediction. Furthermore, the overlook of long-term memory features could lead to biases in model parameter estimation and testing of time series properties. The classical linear Autoregressive-Generalized Autoregressive Conditional Heteroskedasticity (AR-GARCH) model has a narrow parameter range, and the moment conditional requirements for parameter estimation are relatively strict, limiting its applicability and prediction accuracy in modeling and predicting daily streamflow. Under the premise of long-term memory, a dual-threshold double autoregressive (DTDAR) model is proposed to capture the non-linear patterns in streamflow series. Using 15 hydrological stations in the Yellow River basin in China as an example, DTDAR models are compared with AR-GARCH and long short-term memory (LSTM) models to assess their applicability and predictive ability. The results indicate that the DTDAR models have a stronger predictive ability for daily streamflow than the AR-GARCH-type and LSTM models. The nonlinear changes of the daily streamflow time series are reflected in multiple linear structures by adding the threshold, improving the accuracy of the single linear structure method. The NSE values of the FDTDAR and TAR-GARCH models are higher than those of the DAR and AR-GARCH models by 0.013–0.556 and 0.031–0.582, respectively. Compared to the normal distribution, the Student's t distribution for residuals is a better choice for predicting daily streamflow time series in the study area. This study enriches the stochastic hydrological models and improves the accuracy of streamflow prediction.