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Modélisation GARCH multivariée pour les variables climatiques et hydrologiques.

Modarres, Reza (2013). Modélisation GARCH multivariée pour les variables climatiques et hydrologiques. Thèse. Québec, Université du Québec, Institut national de la recherche scientifique, Doctorat en sciences de l'eau, 408 p.

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Résumé

Hydrologic time series modeling usually includes linear approaches which model the time varying mean or the conditional mean of the hydrologic variables. However, most of the hydrologic variables show nonlinear variations through time. The nonlinear modeling of hydrologic variables has received considerable attentions in recent decades. Although a number of nonlinear models have been presented in the literature, the nonlinear time series models have not been sufficiently applied in hydrology and climatology. As the hydroclimatic variables change and influence each other within a temporal and spatial scale, it is essential to apply the appropriate multivariate models which take into account the nonlinear relationships between hydrologic variables through space and time. The main goal of this study is to propose and develop a class of multivariate time series models called 'Multivariate Generalized Autoregressive Conditional Heteroscedasticity' (MGARCH) model, usually applied in financial time series modeling, for different hydrologic and climatic variables. The MGARCH modeling approach is used to model the conditional variance-covariance or volatility-covolatility of hydroclimatic variables. This study presents different types of univariate asymmetric GARCH models such as EGARCH, PGARCH and TGARCH models and multivariate GARCH models such as VECH, BEKK, CCC and DCC models to consider this time varying conditional variance- Covariance relationship between different hydrologic variables. Moreover, different stationarity and nonlinearity tests are also applied in this study to test and compare different hydrologic and climatic variables and their variance-covariance structure. The asymmetric GARCH models for streamflow heteroscedastict modeling indicate a better performance for exponential GARCH (EGARCH) model than the ARIMA models while other asymmetric models (PGARCH, TGARCH) did not show a better performance. However, it is also observed that the adding a GARCH model to the SARIMA model for rainfall time series modeling does not improve the accuracy of estimation, especially when the Box-Cox transformation is applied on rainfall time series. The univariate GARCH model for testing the volatility change of SOI shows a remarkable change in the short run persistency of the conditional variance of SOI and shows more extreme conditional variances in recent decades. The diagonal VECH and CCC models adapted and developed to investigate the effect of the variance of rainfall on the streamflow show that rainfall has a strong conditional variance while runoff shows a short run conditional variance. The covariance between rainfall and runoff shows a long run characteristic and a high degree of nonlinearity. This characteristic may be due to the effect of physical catchment features on rainfall-runoff process. It seems that the CCC model which assumes a constant rainfall-runoff correlation is not valid for rainfall-runoff process. It is also observed that the MGARCH(l,l) model is sufficient for conditional variance-covariance modeling comparing to higher order models, i.e MGARCH(2,2) model. The advantage of developing the MGARCH approach for drought analysis is also investigated in this research. Drought is a climate phenomenon usually related to large atmospheric circulations. The diagonal VECH and BEKK approaches showed that the covariance structure between drought and atmospheric oscillations (NAO and SOI) is not strong and mostly related to the cross products of shocks rather than the covariances at the previous time steps. The time varying conditional correlation between drought and atmospheric indices do not show a significant change and trend during 1954-2010. The MGARCH approach is also adapted for modeling the variance-covariance structure between temperature and output of GCM models which are applied for downscaling. The diagonal VECH and DCC model indicate short run persistence between GCM predictors and temperature time series. Except some GCMs such as specific humidity and 2m temperature, which have a strong covariance association with maximum and minimum temperature, other GCMs do not influence the variance of temperature data. The conditional correlation between GCMs and temperature time series do not show a significant upward or downward trend during 1980 to 2000. In the field of social and public health and medical treatment, hip fracture is assumed to be largely related to different climate conditions. Adapting the CCC MGARCH method in the present study show a high impact of severe weather condition on hip fracture rate in Montreal region. It is observed that the snow depth, minimum temperature and day length are the most effective weather factors on hip fracture. It can be observed that the association between hip fracture incidence and climate variables is very weak or linear for small numbers of hip fracture incidences while this association (climate effect on hip fracture rate) increases exponentially and in a nonlinear fashion for the higher hip fracture rate values and harsh weather conditions.This research also shows that the hydrologic and climatologic variables exhibit nonlinear temporal variation which the MGARCR model seems to be an interesting approach to be developed, investigated and applied in order to capture this nonlinear characteristic of hydrologic and climatic variables. We can see that daily time series show a higher degree of nonlinearity and the rainfall-runoff process indicates the highest nonlinearity among all hydroclimatic process in this study. In addition, the conditional variance-covariance structures show stationarity for all process. However, some trend nonstationarity is observed for sometime series such as temperature and their association to other variables. Finally, the proposed methods in this study give us the opportunity to have a closer look at the time varying second order moment of different hydrologic and climatic variables and to develop our understanding of their relationship. However, the univariate GARCR models show both advantage and disadvantage over univariate linear models such as ARIMA and SARIMA models. A high number of parameters also remains the main disadvantage of multivariate GARCR models.

Type de document: Thèse
Directeur de mémoire/thèse: Ouarda, Taha B.M.J.
Mots-clés libres: ACHG; GARCH; modélisation non linéaire; hydrologie; climat
Centre: Centre Eau Terre Environnement
Date de dépôt: 05 nov. 2013 21:28
Dernière modification: 24 nov. 2015 21:16
URI: http://espace.inrs.ca/id/eprint/1694

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