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Partager le résultat de cette recherche Interroger des sources externesStatistique asymptotique dans les modèles bilinéaires À changement de régime Markovien / Ahmed Ghezal
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
MathématiquesTags : 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 ?-Mixing Invertibility Quasi-maximum likelihood Strong consistency q dependent Markov chain minimum distance estimation "?????? ARMA ????????? ???????? ??????? ???????? ??????????? ??????????? ?? ?????? ??????? ???????
????? ????? ?????? ????? ???? -q ???? ??????? ???-???????? ?????? ??????? ?????? -? ???????
?????? ???????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 : Permalink : https://bu.umc.edu.dz/md/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 . - [S.l.] : جامعة الإخوة منتوري قسنطينة, 2015 . - 72 f. ; 30 cm.
2 copies imprimées disponibles
Langues : Français (fre)
Catégories : Français - Anglais
MathématiquesTags : 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 ?-Mixing Invertibility Quasi-maximum likelihood Strong consistency q dependent Markov chain minimum distance estimation "?????? ARMA ????????? ???????? ??????? ???????? ??????????? ??????????? ?? ?????? ??????? ???????
????? ????? ?????? ????? ???? -q ???? ??????? ???-???????? ?????? ??????? ?????? -? ???????
?????? ???????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 : Permalink : https://bu.umc.edu.dz/md/index.php?lvl=notice_display&id=9921 Exemplaires (1)
Code-barres Cote Support Localisation Section Disponibilité GHE/6702 GHE/6702 Thèse Bibliothèque principale Thèses Disponible
Titre : Inférence statistique dans les équations différentielles stochastiques Type de document : texte imprimé Auteurs : Fateh Merahi, Auteur ; Abdelouahab Bibi, Directeur de thèse Editeur : جامعة الإخوة منتوري قسنطينة Année de publication : 2018 Importance : 135 f. Format : 30 cm. Note générale : 2 copies imprimées disponibles
Langues : Français (fre) Catégories : Français - Anglais
MathématiquesTags : Processus bilinéaire à temps continu Représentation spectrale Solution de Itô Stationnarité Propriété de longue mémoire Propriété de Taylor Processus quadratique Estimation GMM Estimations de maximum vraisemblance Consistance forte Normalité Asymptotique Continuous-time bilinear processes Spectral representation Itô’s solution Stationarity long memory property Taylor effect Quadratic processes (G) MM estimation YuleWalker estimates Maximum Likelihood estimates Strong consistency Asymptotic Normality ????? ???????? ????? ?????? ?????? ?????? ????? ???? ?? ????
????????? ?? ????? ????? ????? ????? ?????? ??? ?????? ?????? ???? ?????? ?????? ????? ???????? ?????? ??????? ?????? ??????? ???????Index. décimale : 510 Mathématiques Résumé : In this thesis, we are studying a class of continuous-time bilinear processes (COBL(1,1))
generated by some stochastic differential equations where we have investigate some probabilistic
properties and statistical inference. We use Itô approach for studying the L2 structure of the
COBL(1,1) process and its powers for any order with time varying coefficients. Furthermore we
prove that these results can be obtained by using the transfer functions approach, moreover, by
the spectral representation of the process, we give also conditions for the stability of moments,
in particular the moments of the quadratic process provide us to checking the presence of the so
called Taylor property for COBL(1,1) process. In a second part of this thesis, we use the results
of the first part and we propose some methods of estimation for involving unknown parameters,
so, we starting by the moments method (MM) to estimate the parameters by two methods,
taking into consideration the relation that exists between the moments of the process and its
quadratic version and those associate with the incremented processes where we have showed
that the resulting estimators are strongly consistent and asymptotically normal under certain
conditions. Using the linear representation of COBL(1,1) process, we are able to propose three
other methods, one is in frequency domain and the rest are in time domain and we prove the
asymptotic properties of the proposed estimators. Simulation studies are presented in order to
illustrate the performances of the different estimators, furthermore, this methods are used to
model some real data such as the exchanges rate of the Algerian Dinar against the US-dollar
and against the single European currency and the electricity consumption sampled each 15mn
in Algeria.
Diplôme : Doctorat en sciences En ligne : ../theses/math/MER7232.pdf Format de la ressource électronique : Permalink : https://bu.umc.edu.dz/md/index.php?lvl=notice_display&id=10802 Inférence statistique dans les équations différentielles stochastiques [texte imprimé] / Fateh Merahi, Auteur ; Abdelouahab Bibi, Directeur de thèse . - [S.l.] : جامعة الإخوة منتوري قسنطينة, 2018 . - 135 f. ; 30 cm.
2 copies imprimées disponibles
Langues : Français (fre)
Catégories : Français - Anglais
MathématiquesTags : Processus bilinéaire à temps continu Représentation spectrale Solution de Itô Stationnarité Propriété de longue mémoire Propriété de Taylor Processus quadratique Estimation GMM Estimations de maximum vraisemblance Consistance forte Normalité Asymptotique Continuous-time bilinear processes Spectral representation Itô’s solution Stationarity long memory property Taylor effect Quadratic processes (G) MM estimation YuleWalker estimates Maximum Likelihood estimates Strong consistency Asymptotic Normality ????? ???????? ????? ?????? ?????? ?????? ????? ???? ?? ????
????????? ?? ????? ????? ????? ????? ?????? ??? ?????? ?????? ???? ?????? ?????? ????? ???????? ?????? ??????? ?????? ??????? ???????Index. décimale : 510 Mathématiques Résumé : In this thesis, we are studying a class of continuous-time bilinear processes (COBL(1,1))
generated by some stochastic differential equations where we have investigate some probabilistic
properties and statistical inference. We use Itô approach for studying the L2 structure of the
COBL(1,1) process and its powers for any order with time varying coefficients. Furthermore we
prove that these results can be obtained by using the transfer functions approach, moreover, by
the spectral representation of the process, we give also conditions for the stability of moments,
in particular the moments of the quadratic process provide us to checking the presence of the so
called Taylor property for COBL(1,1) process. In a second part of this thesis, we use the results
of the first part and we propose some methods of estimation for involving unknown parameters,
so, we starting by the moments method (MM) to estimate the parameters by two methods,
taking into consideration the relation that exists between the moments of the process and its
quadratic version and those associate with the incremented processes where we have showed
that the resulting estimators are strongly consistent and asymptotically normal under certain
conditions. Using the linear representation of COBL(1,1) process, we are able to propose three
other methods, one is in frequency domain and the rest are in time domain and we prove the
asymptotic properties of the proposed estimators. Simulation studies are presented in order to
illustrate the performances of the different estimators, furthermore, this methods are used to
model some real data such as the exchanges rate of the Algerian Dinar against the US-dollar
and against the single European currency and the electricity consumption sampled each 15mn
in Algeria.
Diplôme : Doctorat en sciences En ligne : ../theses/math/MER7232.pdf Format de la ressource électronique : Permalink : https://bu.umc.edu.dz/md/index.php?lvl=notice_display&id=10802 Exemplaires (1)
Code-barres Cote Support Localisation Section Disponibilité MER/7232 MER/7232 Thèse Bibliothèque principale Thèses Disponible
