## 1 Introduction  
Runoff simulation is one of the most important topics in current surface hydrological process research [1]. Runoff is an essential link in the process of the surface water cycle, and is an important indicator that reflects the resource and environmental conditions of the basin. Its changes objectively reflect the changes in regional hydrological processes and water resources' inventory [2, 3]. The hydrological model is an excellent instrument for runoff simulation, analysis, and calculation, and it is a crucial way to explore and understand the water cycle and hydrological processes. The hydrological model also simulates the main characteristics of the rainfall-runoff process by generalizing the complex water cycle process, which is important for water resources development and utilization, flood prevention and mitigation, urban planning, vegetation impacts and watershed response to human activities, and many other aspects [4, 5, 6, 7]. With the wide application of hydrological models,the issue of how to improve the accuracy of rainfall-runoff simulations has attracted more and more attention from scholars and has increasingly become one of the critical topics in hydrology research [4]. Modern time series analysis originated in 1927 with the autoregressive (AR) model proposed by the British statistician [PERSON] [8]. Together with the moving average (MA) model and the ARMA model proposed by [PERSON] in 1931, this model formed the basis of time series analysis and is still heavily used today [9]. With the continuous development of the theory and application of time series analysis, time series models are used in many fields such as finance, e-commerce, information and data mining. The common time series models include: (1) autoregressive (AR) models, moving average (MA) models, and autoregressive integrated moving average (ARIMA) models based on traditional probabilistic statistical methods [10]; (2) the BP neural network model and long and short-term memory (LSTM) neural network models based on machine learning algorithms [11; 12]; and (3) the Prophet model based on time series decomposition and machine learning fitting. The use of error correction models to improve the accuracy of hydrological model forecasts is an effective tool [13], and time series models have also played a significant role in this regard. [PERSON] et al. [14] used the meta-Gaussian model to predict the posterior distribution of errors to obtain the predicted flow interval results with a certain confidence. [PERSON] et al. [15] employed the ARMA-GARCH model with the heteroscedasticity of the hydrological sequence to post-process the error series of runoff simulated by the Xianjiang model to obtain real-time flood prediction results, which significantly improved the prediction accuracy. [PERSON] et al. [16] applied the Bayesian forecasting system (BFS) and hydrologic uncertainty processor (HUP) to the Baishan Reservoir basin to obtain a posterior distribution of predicted flow to reduce simulation uncertainty. [PERSON] et al. [17] took the Shuibuya upstream watershed as the study area and established the regression model of distributed hydrological model DEM-based distributed rainfall-runoff model (DDRM) simulation results for the real-time correction of the runoff simulation. The results show that the regression model, to a certain extent, makes up for the actual application of distributed hydrological model due to lack of information and the decline in precision. [PERSON] et al. [13] used two real-time correction technologies, the autoregressive (AR) model and the entire-process joint correction method (EPJC), to predict and correct the runoff error of the Xianjiang model in order to reduce the runoff prediction error in the Dadu River Basin, thus improving the actual forecasting ability of the hydrological model.