Impact of Returns Time Dependency on the Estimation of Extreme Market Risk

The estimation of Value-at-Risk generally used models assuming independence. However, financial returns tend to occur in clusters with time dependency. In this paper we study the impact of negligence of returns dependency in market risk assessment. The main methods which take into account returns dependency to assess market risk are: Declustering, Extremal index and Time series-Extreme Value The- ory combination. Results shows an important reduction of the estimation error under dependency assumption. For real data, methods which take into account returns dependency have generally the best performances.Value-at-Risk, Market risk, Dependency, Declustering, Extremal index, Time Series-EVT Combination.

On the Prequential Approach for Testing Exponentiality

We present a prequential (predictive-sequential) approach for testing the goodness-of-fit of an exponential distribution when the parameter $\lambda$ is unknown. Instead of using all the available observations, $\lambda$ is estimated by a prequential approach where at each step $i$, only the $i\!-\!1$ first observations are used. We show that this approach provides a sequence of \ks type distances whose expressions do not depend on $\lambda$ and which converge in distribution (under the null hypothesis) to the \ks distribution. This leads to a simple technique for testing the goodness-of-fit of exponential distributions with unknown parameter using standard quantile tables of the \ks distribution. Even if Monte~Carlo simulations show that the prequential test is less powerful than the standard exponentiality test, the developed results represent a first step in the theoretical study of the {\it u-plot} which is a prequential empirical tool commonly used for the validation of reliability-growth models

Quasi-conjugate Bayes estimates for GPD parameters and application to heavy tails modelling

We present a quasi-conjugate Bayes approach for estimating Generalized Pareto Distribution (GPD) parameters, distribution tails and extreme quantiles within the Peaks-Over-Threshold framework. Damsleth conjugate Bayes structure on Gamma distributions is transfered to GPD. Bayes credibility intervals are defined, they provide assessment of the quality of the extreme events estimates. Posterior estimates are computed by Gibbs samplers with Hastings-Metropolis steps. Even if non-informative priors are used in this work, the suggested approach could incorporate informative priors, it brings solutions to the problem of estimating extreme events when data are scarce but expert opinion is available. It is shown that the obtained quasi-conjugate Bayes estimators compare well with the GPD standard estimators on simulated and real data sets

Outils statistiques pour la construction et le choix de modèles en fiabilité des logiciels

This work is mainly concerned with the use of statistical tools for the assessment of software reliability. It provides statistical techniques for the construction and the validation of models taking into account the specific properties of each software. For this, we mainly use Generalized Linear Models (parametric and non-parametric) and Bayesian methods. The final part studies the mathematical problems of validation and choice of Software Reliability models. The predictive-sequential approach is shown to give a simple way of testing the fit of Poisson process models. The obtained predictive-sequential test seems to be usable for many Software Reliability models.Ce travail est consacré à l'étude de méthodes statistiques pour l'évaluation de la fiabilité des logiciels. Son but principal est de fournir des outils statistiques permettant de construire et ensuite valider des modèles en tenant compte des spécificités des logiciels étudiés. Pour ce faire deux outils sont utilisés : les modèles linéaires généralisés (paramétriques et non-paramétriques) et l'analyse statistique bayésienne. La deuxième partie de ce travail est consacrée à l'ètude mathématique des problèmes de validation et de choix de modèles en fiabilité des Logiciels. On y étudie entre autres une approche dite "préquentielle" (prédictive-séquentielle) bien adaptée aux tests d'adéquation aux processus de Poisson. Cette approche semble pouvoir se généraliser à un grand nombre de modèles de fiabilité des logiciels

Generalized linear models in software reliability : parametric and semi-parametric approaches

International audienceThe penalized likelihood method is used for a new semi-parametric software reliability model. This new model is a nonparametric generalization of all parametric models where the failure intensity function depends only on the number of observed failures, viz. number-of-failures models (NF). Experimental results show that the semi-parametric model generally fits better and has better 1-step predictive quality than parametric NF. Using generalized linear models, this paper presents new parametric models (polynomial models) that have performances (deviance and predictive-qualities) approaching those of the semi-parametric model. Graphical and statistical techniques are used to choose the appropriate polynomial model for each data-set. The polynomial models are a very good compromise between the nonvalidity of the simple assumptions of classical NF, and the complexity of use and interpretation of the semi-parametric model. The latter represents a reference model that we approach by choosing adequate link and regression functions for the polynomial models

Prequential goodness-of-fit tests for ARA imperfect maintenance models

International audienc

Prequential omnibus goodness-of-fit tests for stochastic processes: A numerical study

International audienceThis article is a contribution to the study of an omnibus goodness-of-fit (Gof) test based on Rosenblatt Probability Integral Transform (RPIT) within Dawid's prequential framework. This Gof test is easy to use since it has a common test statistic (with apparently the same asymptotic distribution) for a wide range of stochastic models. Intensive Monte-Carlo simulations are presented to investigate the behavior of this test for several stochastic models: renewal, autoregressive (AR, ARMA, ARCH, GARCH) and Poisson processes, generalized linear models... These simulations suggest that the RPIT test could be used to test the fit of a wide range of stochastic models but it may be not powerful when compared to Gof tests specifically designed for the tested processes. It is also conjectured that this test is still appropriate for testing the Gof of any discrete-time stochastic process provided that efficient estimators are used

Prequential goodness-of-fit tests for ARA imperfect maintenance models

International audienc

Prequential goodness-of-fit tests for ARA imperfect maintenance models

International audienc