Generalized autoregressive conditional heteroscedasticity modelling of hydrologic time series
Article first published online: 3 JUL 2012
Copyright © 2012 John Wiley & Sons, Ltd.
Volume 27, Issue 22, pages 3174–3191, 30 October 2013
How to Cite
Modarres, R. and Ouarda, T. B. M. J. (2013), Generalized autoregressive conditional heteroscedasticity modelling of hydrologic time series. Hydrol. Process., 27: 3174–3191. doi: 10.1002/hyp.9452
- Issue published online: 2 OCT 2013
- Article first published online: 3 JUL 2012
- Accepted manuscript online: 7 JUN 2012 09:51AM EST
- Manuscript Accepted: 29 MAY 2012
- Manuscript Received: 17 DEC 2011
- nonlinear time series;
- Engle's test;
- SARIMA model;
- Box–Cox transformation
The existence of time-dependent variance or conditional variance, commonly called heteroscedasticity, in hydrologic time series has not been thoroughly investigated. This paper deals with modelling the heteroscedasticity in the residuals of the seasonal autoregressive integrated moving average (SARIMA) model using a generalized autoregressive conditional heteroscedasticity (GARCH) model. The model is applied to two monthly rainfall time series from humid and arid regions. The effect of Box–Cox transformation and seasonal differencing on the remaining seasonal heteroscedasticity in the residuals of the SARIMA model is also investigated. It is shown that the seasonal heteroscedasticity in the residuals of the SARIMA model can be removed using Box–Cox transformation along with seasonal differencing for the humid region rainfall. On the other hand, transformation and seasonal differencing could not remove heteroscedasticity from the residuals of the SARIMA model fitted to rainfall data in the arid region. Therefore, the GARCH modelling approach is necessary to capture the heteroscedasticity remaining in the residuals of a SARIMA model. However, the evaluation criteria do not necessarily show that the GARCH model improves the performance of the SARIMA model. Copyright © 2012 John Wiley & Sons, Ltd.