CIRM - Videos & books Library - Consistent model selection criteria and goodness-of-fit test for common time series models

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Auteurs : Bardet, Jean-Marc (Auteur de la conférence)
CIRM (Editeur )

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Résumé : We study the model selection problem in a large class of causal time series models, which includes both the ARMA or AR($\infty$) processes, as well as the GARCH or ARCH($\infty$), APARCH, ARMA-GARCH and many others processes. To tackle this issue, we consider a penalized contrast based on the quasi-likelihood of the model. We provide sufficient conditions for the penalty term to ensure the consistency of the proposed procedure as well as the consistency and the asymptotic normality of the quasi-maximum likelihood estimator of the chosen model. We also propose a tool for diagnosing the goodness-of-fit of the chosen model based on a Portmanteau test. Monte-Carlo experiments and numerical applications on illustrative examples are performed to highlight the obtained asymptotic results. Moreover, using a data-driven choice of the penalty, they show the practical efficiency of this new model selection procedure and Portemanteau test.

Mots-Clés : Model selection; time series; consistency; BIC; Portmanteau test

Codes MSC :
60K35 - Interacting random processes; statistical mechanics type models; percolation theory

Ressources complémentaires :
https://www.cirm-math.fr/RepOrga/2146/Slides/Bardet.pdf

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Hennenfent, Guillaume

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https://videos.cirm-math.fr/2020-06-02_Bardet.mp4

Informations sur la Rencontre

Nom de la Rencontre : Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2
Organisateurs de la Rencontre : Bogdan, Malgorzata ; Graczyk, Piotr ; Panloup, Fabien ; Proïa, Frédéric ; Roquain, Etienne
Dates : 15/06/2020 - 19/06/2020
Année de la rencontre : 2020
URL de la Rencontre : https://www.cirm-math.com/cirm-virtual-...

Données de citation

DOI : 10.24350/CIRM.V.19640303
Citer cette vidéo: Bardet, Jean-Marc (2020). Consistent model selection criteria and goodness-of-fit test for common time series models. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19640303
URI : http://dx.doi.org/10.24350/CIRM.V.19640303

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Bibliographie

BARDET, Jean-Marc, KAMILA, Kare, KENGNE, William, et al. Consistent model selection criteria and goodness-of-fit test for common time series models. Electronic Journal of Statistics, 2020, vol. 14, no 1, p. 2009-2052. - http://dx.doi.org/10.1214/20-EJS1709

BARDET, Jean-Marc, WINTENBERGER, Olivier, et al. Asymptotic normality of the quasi-maximum likelihood estimator for multidimensional causal processes. The Annals of Statistics, 2009, vol. 37, no 5B, p. 2730-2759. - http://dx.doi.org/10.1214/08-AOS674

DOUKHAN, Paul et WINTENBERGER, Olivier. Weakly dependent chains with infinite memory. Stochastic Processes and their Applications, 2008, vol. 118, no 11, p. 1997-2013. - https://doi.org/10.1016/j.spa.2007.12.004

FRANCQ, Christian et ZAKOIAN, Jean-Michel. GARCH models: structure, statistical inference and financial applications. John Wiley & Sons, 2010. - http://dx.doi.org/10.1002/9780470670057

HSU, Hsiang-Ling, ING, Ching-Kang, TONG, Howell, et al. On model selection from a finite family of possibly misspecified time series models. The Annals of Statistics, 2019, vol. 47, no 2, p. 1061-1087. - http://dx.doi.org/10.1214/18-AOS1706

LI, Wai Keung et MAK, T. K. On the squared residual autocorrelations in non‐linear time series with conditional heteroskedasticity. Journal of Time Series Analysis, 1994, vol. 15, no 6, p. 627-636. - https://doi.org/10.1111/j.1467-9892.1994.tb00217.x

SIN, Chor-Yiu et WHITE, Halbert. Information criteria for selecting possibly misspecified parametric models. Journal of Econometrics, 1996, vol. 71, no 1-2, p. 207-225. - https://doi.org/10.1016/0304-4076(94)01701-8

STRAUMANN, Daniel. Estimation in Conditionally Heteroscedastic Time Series Models. Lectures notes in Statistics 181. 2005. - http://dx.doi.org/10.1007/b138400

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