Cette Note porte sur la structure probabiliste des solutions d'une équation aux différences stochastiques de type GARCH dont les paramètres sont périodiques dans le temps. Nous proposons des conditions nécessaires et suffisantes assurant l'existence de solutions stationnaires, géométriquement ergodiques (au sens périodique) et ayant des moments d'ordre supérieur finis.
This Note examines the probabilistic structure of a GARCH-type stochastic difference equation with periodically time-varying parameters. We propose necessary and sufficient conditions ensuring the existence of stationary solutions, geometrically ergodic (in the periodic sense) and having finite higher-order moments.
Accepté le :
Publié le :
Abdelouahab Bibi 1 ; Abdelhakim Aknouche 2
@article{CRMATH_2009__347_5-6_299_0, author = {Abdelouahab Bibi and Abdelhakim Aknouche}, title = {Propri\'et\'es probabilistes des processus {\protect\emph{GARCH}} p\'eriodiques}, journal = {Comptes Rendus. Math\'ematique}, pages = {299--303}, publisher = {Elsevier}, volume = {347}, number = {5-6}, year = {2009}, doi = {10.1016/j.crma.2009.01.008}, language = {fr}, }
Abdelouahab Bibi; Abdelhakim Aknouche. Propriétés probabilistes des processus GARCH périodiques. Comptes Rendus. Mathématique, Volume 347 (2009) no. 5-6, pp. 299-303. doi : 10.1016/j.crma.2009.01.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.01.008/
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