Exploring the Regional Variance using ARMA-GARCH Models

Recently some generalized autoregressive conditional heteroskedasticity (GARCH) models are proposed and applied to various hydrologic variables to capture and remove the ARCH effect, which has been observed frequently in the residuals from linear autoregressive moving average (ARMA) models fitted to hydrologic time series. As a nonlinear phenomenon of variance behavior, the ARCH effect reveals partially nonstationarity and nonlinearity of hydrological processes. This paper deals with the variation of a river basin using the ARMA-GARCH error model, which combines an ARMA model for modelling the mean behavior and a GARCH model for modelling the variance behavior of the residuals from the ARMA model. Based on the heteroscedasticity of hydrological variable series, the time-varying regional variance is proposed to check the variation of a river basin for the first time. As a study case, the method is applied to four deseasonalized daily discharge series from the middle reach of Yangtze River, China. Through the analyses of the conditional variance in different streamflow series, it is concluded that: (1) The ARCH effect exists in all the studied series which means the stream processes is nonstationary in terms of the variance; (2) The variations of time-varying variances are similar for the series from adjacent hydrological stations, and the similarity degree increases from upstream to downstream; (3) The regional variance is time-varying and can be used for further regional research.