RIBATET Mathieu

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In numerical weather prediction, ensemble forecasting models have become an essential tool to quantify forecast uncertainty and provide probabilistic forecasts. Unfortunately, these models are not perfect and a simultaneous correction of their bias and dispersion is necessary. Contrary to most of the usual techniques, these non-parametric methods allow to take into account the non-linear dynamics of the atmosphere, to add covariates (other meteorological variables, temporal variables, geographical variables...) easily and to select themselves the most useful predictors in the regression. Moreover, we do not make any assumption on the distribution of the variable to be treated. This new approach outperforms existing methods for variables such as temperature and wind speed.For variables known to be difficult to calibrate, such as sexti-hourly precipitation, hybrid versions of our techniques have been created. We show that these hybrid versions (as well as our original versions) are better than the existing methods. The last part of this thesis concerns the evaluation of ensemble forecasts for extreme events. We have shown some properties of the Continuous Ranked Probability Score (CRPS) for extreme values. We have also defined a new measure combining CRPS and extreme value theory, and we examine its coherence on a simulation as well as in an operational framework.The results of this work are intended to be inserted within the forecasting and verification chain at Météo-France.

It is known that the historical observed returns used to estimate the expected return provide poor guides to predict the future returns. Consequently, the optimal portfolio weights are extremely sensitive to the return assumptions used. Getting information about the future evolution of different asset returns, could help the investors to obtain more efficient portfolio. The solution will be reached by estimating the portfolio risk by conditional variance or conditional semivari-ance. This strategy allows us to take advantage of returns prediction which will be obtained by nonparametric univariate methods. Prediction step uses kernel estimation of conditional mean. Application on the Chinese and the American markets are presented and discussed.

In this paper, we consider the problem of portfolio optimization. The risk will be measured by conditional variance or semivariance. It is known that the historical returns used to estimate expected ones provide poor guides to future returns. Consequently, the optimal portfolio asset weights are extremely sensitive to the return assumptions used. Getting informations about the future evolution of different asset returns, could help the investors to obtain more efficient portfolio. The solution will be reached under conditional mean estimation and prediction. This strategy allows us to take advantage from returns prediction which will be obtained by nonparametric univariate methods. Prediction step uses kernel estimation of conditional mean. Application on Chinese and American markets are presented and discussed.

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Although the last decades have seen many developments on max-stable processes, little is known on the limiting distribution of exceedances of stochastic processes. Paralleling the univariate extreme value theory, this work focuses on threshold exceedances of a stochastic process and their connections with regularly varying and generalized Pareto processes. More precisely we define an exceedance through a cost functional ` and show that the limiting (rescaled) distribution is a simple `–Pareto process whose spectral measure can be characterized. Several equivalent constructions for `–Pareto processes are given using either a constructive approach, either an homogeneity property or a peak over threshold stability. We also provide an estimator of the spectral measure and give some examples.

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We use statistical models for mean and extreme values of total column ozone to analyze "fingerprints" of atmospheric dynamics and chemistry on long-term ozone changes at northern and southern mid-latitudes on grid cell basis. At each grid cell, the r-largest order statistics method is used for the analysis of extreme events in low and high total ozone (termed ELOs and EHOs, respectively), and an autoregressive moving average (ARMA) model is used for the corresponding mean value analysis. In order to describe the dynamical and chemical state of the atmosphere, the statistical models include important atmospheric covariates: the solar cycle, the Quasi-Biennial Oscillation (QBO), ozone depleting substances (ODS) in terms of equivalent effective stratospheric chlorine (EESC), the North Atlantic Oscillation (NAO), the Antarctic Oscillation (AAO), the El Niño/Southern Oscillation (ENSO), and aerosol load after the volcanic eruptions of El Chichón and Mt. Pinatubo. The influence of the individual covariates on mean and extreme levels in total column ozone is derived on a grid cell basis. The results show that "fingerprints", i.e., significant influence, of dynamical and chemical features are captured in both the "bulk" and the tails of the statistical distribution of ozone, respectively described by mean values and EHOs/ELOs. While results for the solar cycle, QBO, and EESC are in good agreement with findings of earlier studies, unprecedented spatial fingerprints are retrieved for the dynamical covariates. Column ozone is enhanced over Labrador/Greenland, the North Atlantic sector and over the Norwegian Sea, but is reduced over Europe, Russia and the Eastern United States during the positive NAO phase, and vice-versa during the negative phase. The NAO's southern counterpart, the AAO, strongly influences column ozone at lower southern mid-latitudes, including the southern parts of South America and the Antarctic Peninsula, and the central southern mid-latitudes. Results for both NAO and AAO confirm the importance of atmospheric dynamics for ozone variability and changes from local/regional to global scales.

The practitioner, when predetermining flood flows, is often confronted with a limited data set. In our research work, we have proposed three new probabilistic models specially designed for the estimation of flood regime characteristics in a partially gauged context. Among these models, two of them are so-called regional models, i.e. integrating information coming from stations having a behavior considered similar to the one of the studied site. These models, based on Bayesian theory, showed a great robustness to the degree of heterogeneity of the sites belonging to the region. Similarly, it appeared that for the estimation of high quantiles (T > 50 years), the idea of a regional parameter controlling the extrapolation is relevant but must be integrated in a flexible way and not imposed within the likelihood. Since the most valuable information available to the practitioner is that from the study site, the third proposed model reverts to estimating only from data contemporary with the study site. This new model uses richer information than that obtained from a classical sampling of maximum v.a.i.id. since the whole chronicle is exploited. Therefore, even with only five years of record and thanks to a modeling of the dependence between successive observations, the size of the exploited samples is then much more important. We have shown that for the estimation of flood quantiles, this model clearly outperforms the local approaches classically used in hydrology. This result is all the more true when the return periods become important. Finally, by construction, this approach also allows to obtain a probabilistic estimation of the flood dynamics.