A comparison of several cyclo-stationary and fractionally differenced time-varying autoregressive models in runoff simulation and prediction

Due to the far-reaching effects of climate change and human activities, hydrological processes exhibit cyclostationarity and long-term memory. Neither the traditional autoregressive (AR) nor the time-varying autoregressive (TVAR) model can comprehensively characterize these runoff characteristics, leading to poor model prediction performance. We propose a novel fractionally differenced TVAR model based on the de-seasonality method (FDTVARD) to better capture the above runoff characteristics and achieve improved runoff simulation and prediction accuracy. We first compare the effects of two covariates, time and lagged target variables, on the performance of the FDTVARD model. The FDTVARD model is compared with the AR model based on the deseasonality method (ARD), fractionally differenced ARD (FDARD) and TVAR model based on the deseasonality method (TVARD), and the model performance is evaluated using daily runoff data from seven hydrological stations in the Yellow River Basin, China. The results show that (1) the FDTVARD model has the simplest model form and yields the best simulation and forecasting performance, and the optimal covariate is time. (2) Considering only the time-varying nature of the model coefficients improves the ARD model prediction performance more than considering only the long-term memory of the runoff series. Considering both factors improve the simulation and prediction performance of the ARD model more than considering only one factor. The study findings could facilitate improvements in the prediction accuracy of stochastic hydrological models.