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

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Authors : Bardet, Jean-Marc (Author of the conference)
CIRM (Publisher )

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Abstract : 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.

Keywords : Model selection; time series; consistency; BIC; Portmanteau test

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

Additional resources :
https://www.cirm-math.fr/RepOrga/2146/Slides/Bardet.pdf

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Film maker :

Hennenfent, Guillaume

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

Information on the Event

Event Title : Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2
Event Organizers : Bogdan, Malgorzata ; Graczyk, Piotr ; Panloup, Fabien ; Proïa, Frédéric ; Roquain, Etienne
Dates : 15/06/2020 - 19/06/2020
Event Year : 2020
Event URL : https://www.cirm-math.com/cirm-virtual-...

Citation Data

DOI : 10.24350/CIRM.V.19640303
Cite this video as: 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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Bibliography

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

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