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.
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.
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