Nous étudions le problème dʼestimation dans les séries temporelles fortement dépendantes. Nous considérons les processus Gegenbaeur autorégressifs à moyenne mobile (GARMA) à k facteurs pour les modéliser et nous estimons leurs paramètres par la méthode du minimum de distance de Hellinger. Nous établissons la consistance de lʼestimateur et la normalité asymptotique pour un certain choix de fenêtre de lissage.
We address the problem of parameter estimation of long memory time series. We consider k-factors Gegenbauer Autoregressive Moving Average (k-GARMA) processes and we estimate their parameters by the minimum Hellinger distance estimator. We establish the consistency of the estimator and the asymptotic normality for some bandwidth choice.
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@article{CRMATH_2012__350_19-20_925_0, author = {Kouam\'e, Euloge F. and Hili, Ouagnina}, title = {A new time domain estimation of k-factors {GARMA} processes}, journal = {Comptes Rendus. Math\'ematique}, pages = {925--928}, publisher = {Elsevier}, volume = {350}, number = {19-20}, year = {2012}, doi = {10.1016/j.crma.2012.10.019}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2012.10.019/} }
TY - JOUR AU - Kouamé, Euloge F. AU - Hili, Ouagnina TI - A new time domain estimation of k-factors GARMA processes JO - Comptes Rendus. Mathématique PY - 2012 SP - 925 EP - 928 VL - 350 IS - 19-20 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2012.10.019/ DO - 10.1016/j.crma.2012.10.019 LA - en ID - CRMATH_2012__350_19-20_925_0 ER -
%0 Journal Article %A Kouamé, Euloge F. %A Hili, Ouagnina %T A new time domain estimation of k-factors GARMA processes %J Comptes Rendus. Mathématique %D 2012 %P 925-928 %V 350 %N 19-20 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2012.10.019/ %R 10.1016/j.crma.2012.10.019 %G en %F CRMATH_2012__350_19-20_925_0
Kouamé, Euloge F.; Hili, Ouagnina. A new time domain estimation of k-factors GARMA processes. Comptes Rendus. Mathématique, Tome 350 (2012) no. 19-20, pp. 925-928. doi : 10.1016/j.crma.2012.10.019. http://archive.numdam.org/articles/10.1016/j.crma.2012.10.019/
[1] Minimum Hellinger distance estimates for parametric models, Ann. Statist., Volume 5 (1977) no. 2, pp. 445-463
[2] A generalized fractionally differencing approach in long memory modelling, Lith. Math. J., Volume 35 (1995), pp. 53-65
[3] On generalized fractional processes, J. Time Series Anal., Volume 10 (1989), pp. 233-257
[4] On the estimation of nonlinear time series models, Stochastics Stochastics Rep., Volume 52 (1995), pp. 207-226
[5] On the estimation of β-ARCH model, Statist. Probab. Lett., Volume 45 (1999), pp. 285-293
[6] Minimum distance estimation of k-factors GARMA processes, Statist. Probab. Lett., Volume 78 (2008), pp. 3254-3261
[7] T. Takada, Robust estimation of latent variable models with application to stochastic volatility models, Faculty of Business Osaka-city University, Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan, 2007.
[8] A k-factor GARMA long-memory model, J. Time Series Anal., Volume 19 (1998) no. 5, pp. 485-504
[9] Kernel density estimation for linear processes, Ann. Statist., Volume 30 (2002), pp. 1441-1459
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