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Empirical spectral processes for stationary state space models

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Multi angle
Auteurs : Fasen-Hartmann, Vicky (Auteur de la Conférence)
CIRM (Editeur )

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Résumé : In this talk, we consider function-indexed normalized weighted integrated periodograms for equidistantly sampled multivariate continuous-time state space models which are multivariate continuous-time ARMA processes. Thereby, the sampling distance is fixed and the driving Lévy process has at least a finite fourth moment. Under different assumptions on the function space and the moments of the driving Lévy process we derive a central limit theorem for the function-indexed normalized weighted integrated periodogram. Either the assumption on the function space or the assumption on the existence of moments of the Lévy process is weaker. The results can be used to derive the asymptotic behavior of the Whittle estimator and to construct goodness-of-fit test statistics as the Grenander-Rosenblatt statistic and the Cramér-von Mises statistic.

Keywords : Cramér-von mises test; empirical spectral process; functional central limit theorem; good- ness of fit test; Grenander-Rosenblatt test; MCARMA process; periodogram, state space model

Codes MSC :
62F03 - Hypothesis testing
62F12 - Asymptotic properties of estimators
62M10 - Time series, auto-correlation, regression, etc.

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 25/07/2022
    Date de captation : 04/07/2022
    Sous collection : Research talks
    arXiv category : Statistics Theory
    Domaine : Probability & Statistics
    Format : MP4 (.mp4) - HD
    Durée : 00:40:10
    Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2022-07-04-Faesen.mp4

Informations sur la Rencontre

Nom de la rencontre : Heavy Tails, Long-Range Dependence, and Beyond / Queues lourdes, dépendance de long terme et  au-delà
Organisateurs de la rencontre : Biermé, Hermine ; Kulik, Rafal ; Mikosch, Thomas ; Wang, Yizao ; Wintenberger, Olivier
Dates : 04/07/2022 - 08/07/2022
Année de la rencontre : 2022
URL Congrès : https://conferences.cirm-math.fr/2633.html

Données de citation

DOI : 10.24350/CIRM.V.19937703
Citer cette vidéo: Fasen-Hartmann, Vicky (2022). Empirical spectral processes for stationary state space models. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19937703
URI : http://dx.doi.org/10.24350/CIRM.V.19937703

Voir aussi

Bibliographie

  • FASEN-HARTMANN, Vicky et MAYER, Celeste. Empirical spectral processes for stationary state space processes. arXiv preprint arXiv:2202.12589, 2022. - https://doi.org/10.48550/arXiv.2202.12589

  • BARDET, Jean‐Marc, DOUKHAN, Paul, et LEÓN, José Rafael. Uniform limit theorems for the integrated periodogram of weakly dependent time series and their applications to Whittle's estimate. Journal of Time Series Analysis, 2008, vol. 29, no 5, p. 906-945. - https://doi.org/10.1111/j.1467-9892.2008.00588.x

  • DAHLHAUS, Rainer. Empirical spectral processes and their applications to time series analysis. Stochastic Processes and their Applications, 1988, vol. 30, no 1, p. 69-83. - https://doi.org/10.1016/0304-4149(88)90076-2

  • DAHLHAUS, Rainer et POLONIK, Wolfgang. Empirical spectral processes for locally stationary time series. Bernoulli, 2009, vol. 15, no 1, p. 1-39. - http://dx.doi.org/10.3150/08-BEJ137

  • MIKOSCH, Thomas et NORVAIŠA, Rimas. Uniform convergence of the empirical spectral distribution function. Stochastic processes and their applications, 1997, vol. 70, no 1, p. 85-114. - https://doi.org/10.1016/S0304-4149(97)00053-7



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