Stochastic Volatility Modeling of Daily Streamflow Time Series

Under the changing climate, the natural characteristics of hydrological processes are assumed to have been intensified, and the volatility of these processes to have increased significantly. However, the applicability of traditional time series analysis methods and the commonly used Gaussian GARCH (Generalized AutoRegressive Conditional Heteroskedasticity) to streamflow modeling has been limited. Although SV-type (stochastic volatility) models have appeared as competitive alternatives to GARCH-type models owing to their flexibility in modeling volatilities, they have not been applied in hydrological studies. Therefore, this study assesses the applicability of SV models to streamflow modeling using daily streamflow series from 21 hydrological stations in the Yellow River basin. Considering the influence of different types of GARCH and residual distributions, 7 hybrid models with variance fluctuation (fractional autoregressive integrated moving average-GARCH) based on 9 distributions are compared to determine the optimal model for each station. Then 4 SV-type models are introduced and compared with the results of the optimal GARCH-type model to verify their applicability. The results show that: (a) the Gaussian distribution is not applicable in both GARCH-type and SV-type models for modeling daily streamflow; (b) although the GARCH-type models are shown to describe the volatility of streamflow processes and improve the modeling performance, large residuals have been observed in the results of the analysis during the peak flow period; and (c) SV-type models can better describe the streamflow series with time-varying variance and accurately capture the occurrence of peak streamflow. The findings of this study offer practical and promising time series analysis methods for daily streamflow modeling.