Generalized autoregressive conditional heteroscedasticity modelling of hydrologic time series

摘要

The existence of time-dependent variance or conditional variance, commonly called heteroscedasticity, in hydrologic time seriesnhas not been thoroughly investigated. This paper deals with modelling the heteroscedasticity in the residuals of the seasonalnautoregressive integrated moving average (SARIMA) model using a generalized autoregressive conditional heteroscedasticityn(GARCH) model. The model is applied to two monthly rainfall time series from humid and arid regions. The effect of Box–Coxntransformation and seasonal differencing on the remaining seasonal heteroscedasticity in the residuals of the SARIMA model isnalso investigated. It is shown that the seasonal heteroscedasticity in the residuals of the SARIMA model can be removed usingnBox–Cox transformation along with seasonal differencing for the humid region rainfall. On the other hand, transformation andnseasonal differencing could not remove heteroscedasticity from the residuals of the SARIMA model fitted to rainfall data in thenarid region. Therefore, the GARCH modelling approach is necessary to capture the heteroscedasticity remaining in the residualsnof a SARIMA model. However, the evaluation criteria do not necessarily show that the GARCH model improves thenperformance of the SARIMA model. Copyright © 2012 John Wiley & Sons, Ltd.