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H 1 Reconciling the Gaussian and Whittle Likelihood with an application to estimation in the frequency domain

Auteurs : Subba Rao, Suhasini (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : In time series analysis there is an apparent dichotomy between time and frequency domain methods. The aim of this paper is to draw connections between frequency and time domain methods. Our focus will be on reconciling the Gaussia likelihood and the Whittle likelihood. We derive an exact, interpretable, bound between the Gaussian and Whittle likelihood of a second order stationary time series. The derivation is based on obtaining the transformation which is biorthogonal to the discrete Fourier transform of the time series. Such a transformation yields a new decomposition for the inverse of a Toeplitz matrix and enables the representation of the Gaussian likelihood within the frequency domain. We show that the difference between the Gaussian and Whittle likelihood is due to the omission of the best linear predictions outside the domain of observation in the periodogram associated with the Whittle likelihood. Based on this result, we obtain an approximation for the difference between the Gaussian and Whittle likelihoods in terms of the best fitting, finite order autoregressive parameters. These approximations are used to define two new frequency domain quasi-likelihoods criteria. We show these new criteria yield a better approximation of the spectral divergence criterion, as compared to both the Gaussian and Whittle likelihoods. In simulations, we show that the proposed estimators have satisfactory finite sample properties.

    Keywords : biorthogonal transforms; quasi-likehoods; Toeplitz inverse

    Codes MSC :
    62F10 - Point estimation
    62M10 - Time series, auto-correlation, regression, etc.
    62M15 - Spectral analysis of processes


    Ressources complémentaires :
    https://www.cirm-math.fr/RepOrga/2233/Slides/SubbaRao_WhittleGaussian_CIRM.pdf


      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 09/10/2020
      Date de captation : 17/09/2020
      Collection : Probability and Statistics
      Durée : 00:40:38
      Domaine : Probability & Statistics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2020-09-17_Rao.mp4

    Informations sur la Rencontre Virtuelle

    Nom de la rencontre : New Results on Time Series and their Statistical Applications / Séries chronologiques: nouveaux résultats et applications statistiques
    Organisateurs de la rencontre : Bardet, Jean-Marc ; Eckley, Idris ; Fokianos, Konstantinos ; Neumann, Michael H. ; Philippe, Anne
    Dates : 14/09/2020 - 19/09/2020
    Année de la rencontre : 2020
    URL Congrès : https://conferences.cirm-math.fr/2233.html

    Citation Data

    DOI : 10.24350/CIRM.V.19655003
    Cite this video as: Subba Rao, Suhasini (2020). Reconciling the Gaussian and Whittle Likelihood with an application to estimation in the frequency domain.CIRM . Audiovisual resource. doi:10.24350/CIRM.V.19655003
    URI : http://dx.doi.org/10.24350/CIRM.V.19655003


    Voir aussi

    Bibliographie

    1. RAO, Suhasini Subba et YANG, Junho. Reconciling the Gaussian and Whittle Likelihood with an application to estimation in the frequency domain. arXiv preprint arXiv:2001.06966, 2020. - https://arxiv.org/abs/2001.06966

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