Gaussianity and linearity tests of hydrologic time series

Rao, A. Ramachandra; Yu, Gwo-Hsing

doi:10.1007/bf01543286

Cited by 6 publications

(5 citation statements)

References 9 publications

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“…However, it can also be concluded that the annual series is linear as it's p-value is 0.96. This result is in agreement with the statement 'All annual series are linear' 10 . However, the seasonality in the inflow series is assumed to be annual in the previous analyses and it might not be the actual case for in-flow data.…”

Section: Testing For Non-linearitysupporting

confidence: 93%

Effective Water Management in the Mahaweli Reservoir System: Analyzing the Inflow of the Upmost Reservoir

Dilini¹,

Liyanage

Attygalle³

et al. 2014

Proceedings of the International Symposium for Next Generation Infrastructure

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Mahaweli cascaded reservoir system is built contiguous to the Mahaweli river, enhancing the water storage and transferring ability to reinforce the needs of water in accordance with the climatic changes. The foremost requirement of the system is to provide water for irrigation and to produce hydroelectricity to the country that has given rise to conflicting demands of water requirements from the two sectors. Forecasting future water availability is crucial to predict the hydroelectricity generation capacity while maintaining a balance between the provisions of water to both sectors. Therefore, modeling the changes of inflow of the upmost reservoir is substantial to effective water management. Literature has not revealed much evidence for an existence of an accepted statistical model in predicting the inflow, of the system considered. This research is based on the methodologies to test for the seasonality, stochasticity and nonlinearity of the inflow , in advance to fitting a suitable model.

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Section: Testing For Non-linearitysupporting

confidence: 93%

Effective Water Management in the Mahaweli Reservoir System: Analyzing the Inflow of the Upmost Reservoir

Dilini¹,

Liyanage

Attygalle³

et al. 2014

Proceedings of the International Symposium for Next Generation Infrastructure

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“…Because daily meteorological series are usually nonlinear (e.g. Rao and Yu, 1990), and the daily streamflow process is usually perceived as nonlinearly dependent on the magnitude of the rainfall (e.g. Minshall, 1960;Wang et al, 1981), therefore, the major source of nonlinearity in daily streamflow processes probably stems from the nonlinearity in daily precipitation and temperature processes.…”

Section: On the Sources Of Nonlinearitymentioning

confidence: 99%

“…Investigations on nonlinearity and applications of nonlinear models to streamflow series Journal of Hydrology 322 (2006) have received much attention in the past two decades (e.g. Rogers, 1980Rogers, , 1982Rogers and Zia, 1982;Rao and Yu, 1990;Chen and Rao, 2003). Rogers (1980Rogers ( , 1982 and Rogers and Zia (1982) developed a heuristic method to quantify the degree of nonlinearity of drainage basins by using rainfall-runoff data.…”

Section: Introductionmentioning

confidence: 99%

“…Rogers (1980Rogers ( , 1982 and Rogers and Zia (1982) developed a heuristic method to quantify the degree of nonlinearity of drainage basins by using rainfall-runoff data. Rao and Yu (1990) used Hinich bispectrum test (1982) to investigate the linearity and nongaussian characteristics of annual streamflow and daily rainfall and temperature series. They detected nonlinearity in daily meteorological series, but not in annual streamflow series.…”

Section: Introductionmentioning

confidence: 99%

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Testing for nonlinearity of streamflow processes at different timescales

Wang

Vrijling

Gelder

et al. 2006

Journal of Hydrology

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“…Investigations on nonlinearity and applications of nonlinear models to hydrological variables have received considerable attentions in the recent decades. For example, Rao and Yu (1990) investigated the nonlinear characteristics of annual streamflow and daily rainfall and temperature time series. They reported the existence of nonlinearity in daily meteorological series but nonlinearity was not observed in the annual streamflow time series.…”

Section: Introductionmentioning

confidence: 99%

Modelling heteroscedasticty of streamflow times series

Modarres

Ouarda

2013

Hydrological Sciences Journal

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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...

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Gaussianity and linearity tests of hydrologic time series

Cited by 6 publications

References 9 publications

Effective Water Management in the Mahaweli Reservoir System: Analyzing the Inflow of the Upmost Reservoir

Effective Water Management in the Mahaweli Reservoir System: Analyzing the Inflow of the Upmost Reservoir

Testing for nonlinearity of streamflow processes at different timescales

Modelling heteroscedasticty of streamflow times series

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