| 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) |
| Tags : |
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 : |
pdf |
| Permalink : |
http://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)
| Tags : |
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 : |
pdf |
| Permalink : |
http://bu.umc.edu.dz/md/index.php?lvl=notice_display&id=10802 |
|
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