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H 1 Time-frequency analysis of locally stationary Hawkes processes

Auteurs : von Sachs, Rainer (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : In this talk we address generalisation of stationary Hawkes processes in order to allow for a time-evolutive second-order analysis. A formal derivation of a time-frequency analysis via a time-varying Bartlett spectrum is given by introduction of the new class of locally stationary Hawkes process. This model is most appropriate for the analysis of (potentially very) long stretches of observed self-exciting point processes, as introduced in the stationary case by A. Hawkes (1971), in one dimension (temporal) or in a higher dimensional (i.e. spatial) context. Motivated by the concept of locally stationary autoregressive processes, we apply however inherently different techniques to describe and capture the time-varying dynamics of self-exciting point processes in the frequency domain. In particular we derive a stationary approximation of the Laplace transform of a locally stationary Hawkes process. This allows us to define a local intensity function and a local Bartlett spectrum which can be used to compute approximations of first and second order moments of the process. We will also present some insightful simulation studies and propose and discuss preliminary asymptotic results on how to estimate the first and second order structure of the process. Joint work with François Roueff and Laure Sansonnet

    Keywords: locally stationary processes; Hawkes processes; Bartlett spectrum; time frequency analysis; point processes

    Codes MSC :
    46N30 - Applications in probability theory and statistics
    60G55 - Point processes
    62M15 - Spectral analysis of processes

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 02/03/16
      Date de captation : 18/02/16
      Collection : Research talks ; Probability and Statistics
      Format : MP4
      Durée : 00:34:52
      Domaine : Probability & Statistics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2016-02-18_Sachs.mp4

    Informations sur la rencontre

    Nom de la rencontre : Thematic month on statistics - Week 3: Processus / Mois thématique sur les statistiques - Semaine 3 : Processus
    Organisateurs de la rencontre : Boutahar, Mohamed ; Reboul, Laurence
    Dates : 15/02/16 - 19/02/16
    Année de la rencontre : 2016
    URL Congrès : http://conferences.cirm-math.fr/1617.html

    Citation Data

    DOI : 10.24350/CIRM.V.18932603
    Cite this video as: von Sachs, Rainer (2016). Time-frequency analysis of locally stationary Hawkes processes. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18932603
    URI : http://dx.doi.org/10.24350/CIRM.V.18932603


    Voir aussi

    Bibliographie

    1. Roueff, F., von Sachs, R., & Sansonnet, L. (2015). Time-frequency analysis of locally stationary Hawkes processes. - https://hal-institut-mines-telecom.archives-ouvertes.fr/hal-01153882

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