Modeling streamflow time series using nonlinear SETAR-GARCH models

Although hydrological processes are generally nonlinear, linear time series models are commonly adopted in the field of water sciences. Nonlinear approaches such as threshold time series and conditional heteroscedasticity models are still seldom used. In this study, first, two- and three-regime Self-Exciting Threshold Autoregressive (SETAR) models are used to model the mean behavior of daily streamfiows. The residual time series computed from the difference between observations and lag-one time-ahead best-estimates of the fitted models are also obtained. Second, the conditional variance behavior of the residual series obtained from the two- and three regime SETAR models is modeled using the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model. The GARCH model is hence used to capture the time-varying variance behavior of residuals as a nonlinear phenomenon and thus it removes the existence of autoregressive conditional heteroscedasticity so-called ARCH effect. Finally, the performance of SETAR models and their combination with the GARCH model are evaluated. Six deseasonalized daily streamflow series from upstream watershed rivers of Zarrineh Rood dam, in the southern part of Lake Urmia in Iran, are used to illustrate and test the procedure. The McLeod-Li test, a formal test for demonstrating the ARCH effect, indicates that the ARCH effect exists in all residual series, which means that the residuals of streamflow time series are nonstationary in terms of the variance. Results indicate that the hybrid SETAR-GARCH models performed better than the models without GARCH component. Results demonstrate also that the use of nonlinear SETAR and GARCH improves streamflow modeling efficiency by capturing the heteroscedasticity in the residuals of nonlinear threshold time series.