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AUDIOVISUAL MATHEMATICS LIBRARY

AUDIOVISUAL MATHEMATICS LIBRARY

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Consistent model selection criteria and goodness-of-fit test for common time series models

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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.

Keywords : 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
    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 15/06/2020
    Date de captation : 02/06/2020
    Sous collection : Research talks
    arXiv category : Statistics Theory
    Domaine : Probability & Statistics
    Format : MP4 (.mp4) - HD
    Durée : 01:08:34
    Audience : Researchers
    Download : 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
Dates : 15/06/2020 - 19/06/2020
Année de la rencontre : 2020
URL Congrès : https://www.cirm-math.com/cirm-virtual-...

Données de citation

DOI : 10.24350/CIRM.V.19640303
Citer cette vidéo: (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

Voir aussi

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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