, Soit? n une suite d'estimateur des moindres carrés

, Normalité asymptotique), Sous les hypothèses (H1), (H2) et (H3), nous avons, vol.20

, Pour la démonstration, on utilise (6.7) et la proposition suivante

, Proposition 18, Soit p = p (?) 1 et t > 0. Alors la fonction variance de G p,t = G(? ?,t ) est V Gp,t (m) = t 1?p ( e 1 , m ) p?2 · m ? m + e 1 , m · Diag(0, 1, · · · , 1), (6.8) pour tout m = (m 1 , · · · , m k ) dans M Gp

, Puisque toutes les lois de G p,t = G(? ?,t ) sont indéniment divisibles, le résultat suivant fournit les mesures de Lévy modiées ?(? ?,t ) satisfaisant K ?(??,t ) (?) = log det K ??

. Encadrement, perspectives et responsabilités en recherche Nous résumons dans ce chapitre quelques travaux en cours ou des projets de recherche à explorer qui sont dans la continuité de ceux présentés dans ce mémoire. Nous donnons également quelques détails sur des encadrements d'étudiants dans le cadre de mes recherches, ainsi que d'autres aspects, tels que l'implication dans des projets et diverses responsabilités liées à la recherche

, Encadrement et co-encadrement d'étudiants J'encadre régulièrement des mémoires de recherche, des projets et des stages d'étudiants en

, Master 1 et 2 modélisation statistique. J'encade et co-encadre également les thèses suivantes : 1) Co-encadrement à 50% (depuis octobre 2014), avec Saussereau Bruno, de la thèse d'université d'Othman KADMIRI sur les modèles GARCH multivariés à seuil en puissance

, nous envisageons de complèter les travaux sur les modèles PARMA périodiques, dont les propriétés asymptotiques des estimateurs ont été déjà établies par [FRS11], en abordant le problème de la validation de ces modèles an de comparer nos résultats à ceux existant sur les PARMA forts dans la littérature (voir par exemple [McL94, McL95, UD09]). Ensuite, le travail serait d'étendre les travaux de [UD09] au cas mixte des modèles SPARMA (seasonal PARMA) faibles. Cette thèse est à mi-temps, en eet l'étudiant passe 3 à 4 mois maximum chaque année au Laboratoire de Mathématiques de Besançon pour travailler sur la thèse, Encadrement à 100% (depuis octobre 2015) de la thèse d'université de Abdoulkarim ILMI AMIR sur les modèles ARMA faibles saisonniers et/ou périodiques

, Co-encadrement à 50% (depuis octobre 2016), avec Saussereau Bruno, de la thèse d'université de Youssef ESSTAFA sur les modèles FARIMA avec des erreurs dépendantes

, Nous en donnerons plus de détails dans la section suivante sur les travaux en cours. 7.2. TRAVAUX EN COURS ET PERSPECTIVES co-intégrés

, nous nous intéressons à une méthode d'identication dite méthode du coin, an d'identier les ordres de modèles ARMA(p, q) et VARMA(p, q) faibles. Cette méthode est basée sur l'examen du comportement des résidus, où les ordres p et q du modèle sont caractérisés par un coin de 0 dans un tableau (d'où le nom de la méthode), Autres méthodes de sélection des ordres de modèles VARMA faibles En dehors des méthodes basées sur la minimisation d'un critère d'information

. Ensuite, aborder d'autres méthodes d'identication des ordres de modèles ARMA(p, q) et VARMA(p, q) faibles, cette fois basées sur l'examen des corrélogrammes et corrélogrammes partiels comme dans

, Tous les travaux que nous avons développés jusqu'à présent sont des modèles de séries temporelles à temps discret avec erreurs faibles, dont la série des covariances est convergente. Ces types de modèles sont souvent appelés modèles à mémoire courte

, La question qui mériterait d'être examinée est : qu'en est-il dans le cas des modèles ARMA faibles à mémoires longues (c'est-à-dire quand la somme des covariances est divergente) ? Nous tentons d'apporter les premières réponses à cette question dans le cadre de la thèse de Youssef Esstafa débutée en octobre 2016

, Pour modéliser le comportement de mémoire longue, plusieurs modèles peuvent être utilisés. Les processus FARIMA (Fractionally AutoRegressive Integrated Moving Average) sont parmi les modèles les plus connus et les plus utilisés. Ils sont une généralisation des modèles ARIMA (AutoRegressive Integrated Moving Average), pour lesquels le paramètre de différenciation est un entier, Les processus à mémoire longue occupent une place de plus en plus importante dans la littéra-ture des séries temporelles

, On dit qu'un processus stationnaire au second ordre (X t ) t?Z , à valeurs réelles

, Projet bonus qualité recherche (BQR) de 2012-2014, nancé par l'Université de FrancheComté, d'un montant de 5000 euros

, réunissant la majorité des membres de l'équipe de probabilités et statistique du LMB, nancé par la région Bourgogne-Franche-Comté d'un montant de 32000 euros. Ce projet impliquerait également d'autres chercheurs extérieurs à l, 2017.

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