Modelling heteroscedasticty of streamflow times series

Abstract

Time series modelling approaches are useful tools for simulating and forecasting hydrological variables and their change through time. Although linear time series models are common in hydrology, the nonlinear time series model, the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model, has rarely been used in hydrology and water resources engineering. The GARCH model considers the conditional variance remaining in the residuals of the linear time series models, such as an ARMA or an ARIMA model. In the present study, the advantages of a GARCH model against a linear ARIMA model are investigated using three classes of the GARCH approach, namely Power GARCH, Threshold GARCH and Exponential GARCH models. A daily streamflow time series of the Matapedia River, Quebec, Canada, is selected for this study. It is shown that the ARIMA (13,1,4) model is adequate for modelling streamflow time series of Matapedia River, but the Engle test shows the existence of heteroscedasticity in the residuals of the ARIMA model. Therefore, an ARIMA (13,1,4)-GARCH (3,1) error model is fitted to the data. The residuals of this model are examined for the existence of heteroscedasticity. The Engle test indicates that the GARCH model has considerably reduced the heteroscedasticity of the residuals. However, the Exponential GARCH model seems to completely remove the heteroscedasticity from the residuals. The multi-criteria evaluation for model performance also proves that the Exponential GARCH model is the best model among ARIMA and GARCH models. Therefore, the application of a GARCH model is strongly suggested for hydrological time series modelling as the conditional variance of the residuals of the linear models can be removed and the efficiency of the model will be improved.Key words heteroscedasticity; Generalized Autoregressive Conditional Heteroscedasticity (GARCH); Engle test; Exponential GARCH; streamflow time series Modélisation de l'hétéroscédasticité des séries temporelles de débitRésumé Les approches de modélisation des séries temporelles sont des outils utiles pour la simulation et la prévision des variables hydrologiques et de leur évolution à cours du temps. Si les modèles linéaires de séries temporelles sont courants en hydrologie, les modèles non linéaires de séries temporelles, comme le modèle d'hétéroscédasticité conditionnel autorégressif généralisé (GARCH pour l'acronyme anglais), ont rarement été utilisés en hydrologie et en ingénierie des ressources en eau. Le modèle GARCH considère la variance conditionnelle restante des résidus de modèles linéaires de séries temporelles, tels que les modèles ARMA ou ARIMA. Dans la présente étude, nous avons étudié les avantages d'un modèle GARCH par rapport à un modèle linéaire ARIMA en utilisant trois approches de type GARCH, à savoir le modèle GARCH puissance, le modèle GARCH seuil et le modèle GARCH exponentiel. Une série de débits journaliers de la rivière Matapédia, au Québec, Canada, a été choisie pour cette étude. On a montré que le modèle ARIMA (13,1,4...

Enhancing the Prediction Accuracy of Data-Driven Models for Monthly Streamflow in Urmia Lake Basin Based upon the Autoregressive Conditionally Heteroskedastic Time-Series Model

“…It is widely acknowledged that the number and diversity of water-related challenges are large and are expected to increase in the future. So, hydrological modeling can be efficient in order to analyze, understand, and explore solutions for sustainable water management in order to support decision-makers and operational water managers [1]. In recent years, many water-experts have tried to use a range of methods for predicting hydrological components such as streamflow [2].…”

The role of anthropogenic activities in karst spring discharge volatility

“…To further explain the seasonality in the sequence, Modarres and Ouarda () recently used the seasonal ARIMA with GARCH (SARIMA‐GARCH) model to fit the rainfall sequences. Later, Modarres and Ouarda () used the multivariate GARCH model to model the relation between rainfall and run‐off, but the authors did not explore the cause of heteroskedasticity.…”

Assessment of Risk of Rainfall Events with a Hybrid of ARFIMA-GARCH

“…Rainfall analysis have a substantial role in the successful planning, development and implementation of water resource management to evaluate engineering works and environmental problems such as hydropower generation, reservoir operation, flood control and water quality control. Henceforth, an efficient study of rainfall temporal behaviour is the critical mission in hydrology (Modarres & Ouarda, 2013). Most of the traditional methods for measuring the risk related with behaviour of the data set are done through study of the variance or volatility.…”

“…The motivation for using both models comes from the notion that rainfall time series is characterised by both linear and non-linear pattern, therefore neither one of the models can identify the true data generating process DGP (Terui & Dijk, 2002). Modarres and Ouarda (2013) investigated the advantages of non-linear GARCH model over linear ARIMA model using stream flow data of the Matapedia River, Quebec, Canada. The result shows that the linear ARIMA model became inadequate for modelling stream flow time series due to the existence of Heteroskedasticity in the residuals of the ARIMA model as shown by Engle test.…”