Estimation de la matrice de variance asymptotique des estimateurs du QMV de modèles ARMA faibles multivariés

In this Note, we consider the problems of estimating the asymptotic variance of the quasi-maximum likelihood estimator (QMLE) of vector autoregressive moving-average (VARMA) models under the assumption that the errors are uncorrelated but not necessarily independent (i.e. weak VARMA). We first give expressions for the derivatives of the VARMA residuals in terms of the parameters of the models. Secondly we give an explicit expression of the asymptotic variance of the QMLE, in terms of the VAR and MA polynomials, and of the second- and fourth-order structure of the noise. We deduce a consistent estimator of the asymptotic variance of the QMLE.     

Tests portmanteau multivariés d'adéquation de modèles VARMA faibles

In this Note, we consider portmanteau tests for testing the adequacy of vector autoregressive moving-average (VARMA) models under the assumption that the errors are uncorrelated but not necessarily independent. We relax the standard independence assumption to extend the range of application of the VARMA models, allowing us to treat linear representations of general nonlinear processes. We first study the joint distribution of the quasi-maximum likelihood estimator (QMLE) and the noise empirical autocovariances. We thus obtain the asymptotic distribution of residual empirical autocovariances and autocorrelations under weak assumptions on the noise. We deduce the asymptotic distribution of the Ljung–Box (or Box–Pierce) portmanteau statistics for VARMA models with nonindependent innovations. We propose a method to adjust the critical values of the portmanteau tests.     

Estimation de la précision asymptotique dans l'estimation de modèles ARMA faibles

An estimator of the asymptotic covariance matrix of the least squares estimator of ARMA models is proposed. To deal with the ARMA representations of nonlinear processes, the standard strong assumptions on the noise are replaced by a mixing condition on the observed process. The weak consistency of the proposed estimator is proved.     

Convergence de modèles moléculaires vers des modèles de mécanique des milieux continus

The work we present here is focused on the justification of continuum mechanics as a natural asymptotic of molecular theories when the interatomic distance goes to zero. We give a sound theoretical ground to existing models, and derive and next study (apparently) new ones.     

Sur l'estimation des modèles autorégressifs d'ordre multiple de séries temporelles

In this Note, we determine the minimum Hellinger distance estimate of a multiple order autoregressive time series model. Under some assumptions which ensure some probabilistic properties, and under other mild conditions, we establish the asymptotic properties of this estimate. As an example, we consider the exponential autoregressive models.     

Modèles semi-factoriels et modèles de Néron

Let S be the spectrum of a discrete valuation ring with function field K. Let X be a scheme over S. We will say that X is semi-factorial over S if any invertible sheaf on the generic fiber X _K can be extended to an invertible sheaf on X. Here we show that any proper geometrically normal scheme over K admits a proper, flat, normal and semi-factorial model over S. We also construct some semi-factorial compactifications of regular S-schemes, such as Néron models of abelian varieties. The semi-factoriality property for a scheme X/S corresponds to the Néron property of its Picard functor. In particular, one can recover the Néron model of the Picard variety ${{\rm Pic}_{X_K/K,{\rm red}}^0}$ of X _K from the Picard functor Pic _X/S , as in the known case of curves. This provides some information on the relative algebraic equivalence on the S-scheme X.     

Estimation de représentations GARCH faibles

Using an approach based on linear conditional expectations, we define a class of weak ARMA-GARCH representations. The generality of the class is illustrated through a collection of examples. We propose a two-stage estimation procedure based on the minimization of sums of squared linear predictions errors. Strong consistency and asymptotic normality of the estimator are established under ergodic and mixing assumptions.     

Principes de déviations modérées pour des modèles autorégressifs d'ordre p

We establish Moderate deviations principles (MDP) for some stable autoregressive models of order p: first for continuous unbounded additive functionnals of this process, second for the estimation error of the regression function (least-squares estimator in the stable linear case, kernel estimator in the Lipschitz non-linear case).     

Estimation de facteurs de Bayes entre modèles dynamiques non linéaires à espace d'état

The use of nonlinear state space models in the study and control of stochastic dynamic systems is regularly growing. With the new generation of particle filters, efficient filtering methods are now available for the identification of these models. However their statistical selection is still an open problem because of the frequent nonaccessibility of the related likelihoods and the intricate estimation of the latter. This rules out all the usual model comparison information criteria as Akaïke's and unfavour also the efficient methods relying on Bayes factor estimation by MCMC simulations.This Note shows how a convergent nonparametric Bayes factor estimator can be built and used advantageously, as direct application of these new particle filters themselves. To cite this article: J.-P. Vila, I. Saley, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Inférence fondée sur la vraisemblance pour des modèles de records

In a time series $\{X_t,t\ge 1\}$, $X_j$ is said to be an upper record if $X_j>\max ?\{X_1,\dots ,X_{j?1}\}$. Some popular models for records are the Yang–Nevzorov and the Linear Drift models. In this note, we introduce for these models the joint likelihood of the record sequence and the indicators of their occurrence. This likelihood can then be used to obtain estimators of the unknown parameters in the models. It can also be used to derive inferential procedures associated with the selection of a proper model for such data.     

Théorème de Poincaré–Alexander pour les domaines modèles

The Poincaré–Alexander Theorem states that holomorphic mappings defined on an open subset of the unit ball of ${\mathbb{C}}^n$ may, under certain conditions, be extended to a biholomorphism of the unit ball. In a complex manifold, every strongly pseudoconvex homogeneous domain is biholomorphic to the unit ball. In an almost complex manifold, the unit ball is not the only strongly pseudoconvex homogeneous domain. A strongly pseudoconvex homogeneous domain is biholomorphic to a model domain. The aim of this paper is to extend this theorem to model domains.     

Points entiers et modèles des courbes algébriques

LetC: F(X, Y)=0 be an algebraic curve of genus 1, over a number fieldK. In this work we construct a modelG(Z,W)=0 of the curveC, over a fixed number fieldL with , having the following property: ifx, y are algebraic integers ofK withF(x, y)=0, thenz=Z(x, y), w=W(x, y) are algebraic integers ofL withG(z, w)=0. Also, the total degree and the height of the polynomialG are bounded. As an application of this result, we give a reduction of the problem to determine effectively the integer points on a curve of genus 2, over a number field, to the problem to determine effectively the integer solutions of an equation of degree 4, over a number field. Also we consider a family of curvesF(X, Y)=0, defined over a number fieldK, which are cyclic coverings ofP ¹ and we calculate, using our previous results, an explicit upper bound for the height of the integer points ofF(X, Y)=0 overK.

     

Une nouvelle caractérisation des sphères géodésiques dans les espaces modèles

We show that a compact immersed hypersurface of hyperbolic space or an open half-sphere with constant mean curvature and almost constant scalar curvature is a geodesic sphere. To cite this article: J. Roth, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Sur les singularités des séries de fractions rationnelles

Rendiconti del Circolo Matematico di Palermo Series 1 -     

Sur les systèmes distingués de représentants et sur les compléments normaux des sous-groupes de Hall

Sans résumé Présenté par G. Hajós     

Sur les courbes de distribution des probabilités

Sans résumé