Wang et al. (2026) DAR-type model based on “long memory-threshold” structure: a competitor for daily streamflow prediction under changing environment

Identification

• Journal: Hydrology and earth system sciences
• Year: 2026
• Date: 2026-03-25
• Authors: Haoxiang Wang, Songbai Song, G. X. Zhang, Thian Yew Gan, Zhuoyue Peng
• DOI: 10.5194/hess-30-1543-2026

Research Groups

• College of Hydraulic Science and Engineering, Yangzhou University, China
• College of Water Resources and Architectural Engineering, Northwest A & F University, China
• Key Laboratory for Agricultural Soil and Water Engineering in Arid Area of Ministry of Education, Northwest A & F University, China
• Department of Civil and Environmental Engineering, University of Alberta, Canada

Short Summary

This study proposes a novel Fractional-differenced Dual-Threshold Double Autoregressive (FDTDAR) model to improve daily streamflow prediction accuracy under changing environments by capturing non-stationarity, non-linearity, and long-term memory. Applied to the Yellow River basin, the FDTDAR model, particularly with a Student's t-distribution for residuals, demonstrates superior predictive ability compared to AR-GARCH and LSTM models.

Objective

• To improve the prediction accuracy of daily streamflow time series by constructing a novel model with high applicability that can simultaneously capture seasonality, non-stationarity, long-term memory, and nonlinearity of daily streamflow.

Study Configuration

• Spatial Scale: Yellow River Basin, China, with a catchment area of approximately 795,000 km². Data from 15 hydrological stations (mainstream and Weihe River tributary).
• Temporal Scale: Daily streamflow records with a minimum continuous record length of 10 years and 100% data completeness. Data split into 70% for calibration and 30% for out-of-sample testing for one-day-ahead forecasting.

Methodology and Data

• Models used:
  • Proposed: Fractional-differenced Dual-Threshold Double Autoregressive (FDTDAR) model (FDTDAR-n for Gaussian residuals, FDTDAR-t for Student's t-distribution residuals).
  • Benchmark: Autoregressive-Generalized Autoregressive Conditional Heteroskedasticity (AR-GARCH) model, Fractional-differenced Threshold Autoregressive-Generalized Autoregressive Conditional Heteroskedasticity (FTAR-GARCH) model, Long Short-Term Memory (LSTM) network.
  • Methodological components: Seasonal normalization, fractional differencing, dual-threshold structure, quasi-maximum likelihood estimation (QMLE).
• Data sources: Measured daily streamflow time series from 15 hydrological stations in the Yellow River Basin, China. Data available at https://doi.org/10.6084/m9.figshare.26795140.v1 (Wang, 2024).

Main Results

• Daily streamflow series exhibit significant long-term memory, non-stationarity, ARCH effects, and nonlinear behavior.
• The FDTDAR models, particularly when assuming a Student's t-distribution for residuals (FDTDAR-t), demonstrate superior predictive capability for daily streamflow compared to AR-GARCH-type and LSTM models.
• The introduction of a threshold to reflect nonlinear changes in daily streamflow time series through multiple linear structures significantly improves prediction accuracy over single linear structure methods.
• The Nash-Sutcliffe efficiency (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.
• The Student's t-distribution for residuals is a better choice than the traditional normal distribution for predicting daily streamflow time series in the study area, leading to smaller error metrics (Mean Absolute Error, Root Mean Squared Error, Mean Relative Error, Absolute Maximum Error) and larger R² and NSE values.
• Residuals of the FDTDAR and FTAR-GARCH models fall within the 95% confidence intervals, indicating that the models effectively capture the variation structure of the time series, approximating a white noise process.
• The prediction accuracy of the FDTDAR-t model is comparable to, or even slightly higher than, that of the LSTM model.

Contributions

• Proposes a novel Fractional-differenced Dual-Threshold Double Autoregressive (FDTDAR) framework that systematically integrates seasonal normalization, fractional differencing for long-memory modeling, and a dual-threshold structure to capture regime-specific nonlinearities in daily streamflow.
• Enriches the field of stochastic hydrological models by introducing and extending the Double Autoregressive (DAR) model with long-memory and threshold features for hydrological applications.
• Significantly improves the accuracy of daily streamflow prediction by comprehensively addressing the complex characteristics of seasonality, non-stationarity, long-term memory, and nonlinearity.
• Provides evidence for the superior performance of DAR-type models over traditional AR-GARCH-type models in daily streamflow prediction.
• Highlights the importance and effectiveness of using heavy-tailed distributions (specifically Student's t-distribution) for residuals in hydrological time series modeling to better characterize variability.

Funding

• National Natural Science Foundation of China (grant nos. 52509036 and 52079110).

Citation

@article{Wang2026DARtype,
  author = {Wang, Haoxiang and Song, Songbai and Zhang, G. X. and Gan, Thian Yew and Peng, Zhuoyue},
  title = {DAR-type model based on “long memory-threshold” structure: a competitor for daily streamflow prediction under changing environment},
  journal = {Hydrology and earth system sciences},
  year = {2026},
  doi = {10.5194/hess-30-1543-2026},
  url = {https://doi.org/10.5194/hess-30-1543-2026}
}