| Titre : |
Statistique asymptotique dans les modèles bilinéaires À changement de régime Markovien |
| Type de document : |
texte imprimé |
| Auteurs : |
Ahmed Ghezal, Auteur ; A. Bibi, Directeur de thèse |
| Editeur : |
جامعة الإخوة منتوري قسنطينة |
| Année de publication : |
2015 |
| Importance : |
72 f. |
| Format : |
30 cm. |
| Note générale : |
2 copies imprimées disponibles
|
| Langues : |
Français (fre) |
| Catégories : |
Français - Anglais
Mathématiques
|
| Tags : |
Les processus bilinéares à changement de régime markoven stationnarité au sens stricte et au second -ordre la representation ARMA l'ergodicité géométrique B-mélange inversibilité quasi-maximum de vraisemblance la consistance forte chaine de Markov q-dépente l'estimation de la distanceminimale Markov-switching bilinear processes Stationarity second-order
stationarity ARMA representation Geometric ergodicity β-Mixing Invertibility Quasi-maximum likelihood Strong consistency q dependent Markov chain minimum distance estimation "الثبات ARMA السیرورات الثنائیة بتغیرات ماركوفیة الاستقراریة الاستقراریة من الرتبة الثانیة التمثیل
تتعلق بسلسة ماركوف تقدیر الحد -q خلیط العكسیة شبه-الاحتمال الأقصى الكفاءة القویة -β الهندسي
الأدنى للمسافة |
| Index. décimale : |
510 Mathématiques |
| Résumé : |
This thesis investigates some probabilistic properties and statistical applications of general Markovswitching
bilinear processes (MS-BL) that offers remarkably rich dynamics and complex behavior to model non
Gaussian data with structural changes. In these models, the parameters are allowed to depend on unobservable time-homogeneous and stationary Markov chain with finite state space. So, some basic issues concerning this class of models including necessary and sufficient conditions ensuring the existence of ergodic stationary (in some sense) solutions, existence of finite moments of any order and β-mixing are studied. As a consequence, we observe that the local stationarity of the underlying process is neither sufficient nor necessary to obtain the global stationarity. Also, the covariance functions of the process and its power are evaluated and it is shown that the second (resp. higher)-order structure is similar to a some linear processes, and hence admit ARMA representation. We establish also sufficient conditions for the MS-BL model to be β-mixing and geometrically ergodic. We then use these results to give sufficient conditions for β-mixing of a family of MS-GARCH(1,1) processes. A number of illustrative examples are given to clarify the theory and the variety of applications.
Secondary, we illustrate the fundamental problems linked with MS-BL models, i.e., parameters estimation by
considering a maximum likelihood (ML) approach. So, we provide the detail on the asymptotic properties of ML,in particular, we discuss conditions for its strong consistency.
Finally, we used another approach for illustrate the fundamental problems linked with MS-BL models, i.e.,
parameters estimation by a minimum L₂-distance estimator (MDE). So, we provide the detail on the asymptotic
properties of MDE, in particular, we discuss conditions for its consistency and asymptotic normality. Numerical experiments on simulated data sets are presented to highlight the theoretical results.
|
| Diplôme : |
Doctorat en sciences |
| En ligne : |
../theses/math/GHE6702.pdf |
| Format de la ressource électronique : |
pdf |
| Permalink : |
index.php?lvl=notice_display&id=9921 |
Statistique asymptotique dans les modèles bilinéaires À changement de régime Markovien [texte imprimé] / Ahmed Ghezal, Auteur ; A. Bibi, Directeur de thèse . - جامعة الإخوة منتوري قسنطينة, 2015 . - 72 f. ; 30 cm. 2 copies imprimées disponibles
Langues : Français ( fre)
| Catégories : |
Français - Anglais
Mathématiques
|
| Tags : |
Les processus bilinéares à changement de régime markoven stationnarité au sens stricte et au second -ordre la representation ARMA l'ergodicité géométrique B-mélange inversibilité quasi-maximum de vraisemblance la consistance forte chaine de Markov q-dépente l'estimation de la distanceminimale Markov-switching bilinear processes Stationarity second-order
stationarity ARMA representation Geometric ergodicity β-Mixing Invertibility Quasi-maximum likelihood Strong consistency q dependent Markov chain minimum distance estimation "الثبات ARMA السیرورات الثنائیة بتغیرات ماركوفیة الاستقراریة الاستقراریة من الرتبة الثانیة التمثیل
تتعلق بسلسة ماركوف تقدیر الحد -q خلیط العكسیة شبه-الاحتمال الأقصى الكفاءة القویة -β الهندسي
الأدنى للمسافة |
| Index. décimale : |
510 Mathématiques |
| Résumé : |
This thesis investigates some probabilistic properties and statistical applications of general Markovswitching
bilinear processes (MS-BL) that offers remarkably rich dynamics and complex behavior to model non
Gaussian data with structural changes. In these models, the parameters are allowed to depend on unobservable time-homogeneous and stationary Markov chain with finite state space. So, some basic issues concerning this class of models including necessary and sufficient conditions ensuring the existence of ergodic stationary (in some sense) solutions, existence of finite moments of any order and β-mixing are studied. As a consequence, we observe that the local stationarity of the underlying process is neither sufficient nor necessary to obtain the global stationarity. Also, the covariance functions of the process and its power are evaluated and it is shown that the second (resp. higher)-order structure is similar to a some linear processes, and hence admit ARMA representation. We establish also sufficient conditions for the MS-BL model to be β-mixing and geometrically ergodic. We then use these results to give sufficient conditions for β-mixing of a family of MS-GARCH(1,1) processes. A number of illustrative examples are given to clarify the theory and the variety of applications.
Secondary, we illustrate the fundamental problems linked with MS-BL models, i.e., parameters estimation by
considering a maximum likelihood (ML) approach. So, we provide the detail on the asymptotic properties of ML,in particular, we discuss conditions for its strong consistency.
Finally, we used another approach for illustrate the fundamental problems linked with MS-BL models, i.e.,
parameters estimation by a minimum L₂-distance estimator (MDE). So, we provide the detail on the asymptotic
properties of MDE, in particular, we discuss conditions for its consistency and asymptotic normality. Numerical experiments on simulated data sets are presented to highlight the theoretical results.
|
| Diplôme : |
Doctorat en sciences |
| En ligne : |
../theses/math/GHE6702.pdf |
| Format de la ressource électronique : |
pdf |
| Permalink : |
index.php?lvl=notice_display&id=9921 |
|
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