Large deviations of ℓp-blocks of regularly varying time series and applications to cluster inference

Large deviations of ℓ^p-blocks of regularly varying time series and applications to cluster inference

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Standard

Large deviations of ℓ^p-blocks of regularly varying time series and applications to cluster inference. / Buriticá, Gloria; Mikosch, Thomas; Wintenberger, Olivier.

I: Stochastic Processes and Their Applications, Bind 161, 2023, s. 68-101.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Buriticá, G, Mikosch, T & Wintenberger, O 2023, 'Large deviations of ℓ^p-blocks of regularly varying time series and applications to cluster inference', Stochastic Processes and Their Applications, bind 161, s. 68-101. https://doi.org/10.1016/j.spa.2023.03.013

APA

Buriticá, G., Mikosch, T., & Wintenberger, O. (2023). Large deviations of ℓ^p-blocks of regularly varying time series and applications to cluster inference. Stochastic Processes and Their Applications, 161, 68-101. https://doi.org/10.1016/j.spa.2023.03.013

Vancouver

Buriticá G, Mikosch T, Wintenberger O. Large deviations of ℓ^p-blocks of regularly varying time series and applications to cluster inference. Stochastic Processes and Their Applications. 2023;161:68-101. https://doi.org/10.1016/j.spa.2023.03.013

Author

Buriticá, Gloria ; Mikosch, Thomas ; Wintenberger, Olivier. / Large deviations of ℓ^p-blocks of regularly varying time series and applications to cluster inference. I: Stochastic Processes and Their Applications. 2023 ; Bind 161. s. 68-101.

Bibtex

@article{fe163604e4aa46cbb5f9b7e00a0a760d,

title = "Large deviations of ℓp-blocks of regularly varying time series and applications to cluster inference",

abstract = "In the regularly varying time series setting, a cluster of exceedances is a short period for which the supremum norm exceeds a high threshold. We propose to study a generalization of this notion considering short periods, or blocks, with ℓp−norm above a high threshold. Our main result derives new large deviation principles of extremal ℓp−blocks, which guide us to define and characterize spectral cluster processes in ℓp. We then study cluster inference in ℓp to motivate our results. We design consistent disjoint blocks methods to infer features of cluster processes. Our inferential setting promotes the use of large empirical quantiles from the ℓp−norm of blocks as threshold levels which eases implementation and also facilitates comparison for different p>0. Our approach highlights the advantages of cluster inference based on extremal ℓα−blocks, where α>0 is the index of regular variation of the series. We focus on inference of important indices in extreme value theory, e.g., the extremal index.",

keywords = "Cluster processes, Extremal index, Large deviation principles, Regularly varying time series",

author = "Gloria Buritic{\'a} and Thomas Mikosch and Olivier Wintenberger",

note = "Publisher Copyright: {\textcopyright} 2023 The Authors",

year = "2023",

doi = "10.1016/j.spa.2023.03.013",

language = "English",

volume = "161",

pages = "68--101",

journal = "Stochastic Processes and their Applications",

issn = "0304-4149",

publisher = "Elsevier BV * North-Holland",

}

RIS

TY - JOUR

T1 - Large deviations of ℓp-blocks of regularly varying time series and applications to cluster inference

AU - Buriticá, Gloria

AU - Mikosch, Thomas

AU - Wintenberger, Olivier

PY - 2023

Y1 - 2023

N2 - In the regularly varying time series setting, a cluster of exceedances is a short period for which the supremum norm exceeds a high threshold. We propose to study a generalization of this notion considering short periods, or blocks, with ℓp−norm above a high threshold. Our main result derives new large deviation principles of extremal ℓp−blocks, which guide us to define and characterize spectral cluster processes in ℓp. We then study cluster inference in ℓp to motivate our results. We design consistent disjoint blocks methods to infer features of cluster processes. Our inferential setting promotes the use of large empirical quantiles from the ℓp−norm of blocks as threshold levels which eases implementation and also facilitates comparison for different p>0. Our approach highlights the advantages of cluster inference based on extremal ℓα−blocks, where α>0 is the index of regular variation of the series. We focus on inference of important indices in extreme value theory, e.g., the extremal index.

AB - In the regularly varying time series setting, a cluster of exceedances is a short period for which the supremum norm exceeds a high threshold. We propose to study a generalization of this notion considering short periods, or blocks, with ℓp−norm above a high threshold. Our main result derives new large deviation principles of extremal ℓp−blocks, which guide us to define and characterize spectral cluster processes in ℓp. We then study cluster inference in ℓp to motivate our results. We design consistent disjoint blocks methods to infer features of cluster processes. Our inferential setting promotes the use of large empirical quantiles from the ℓp−norm of blocks as threshold levels which eases implementation and also facilitates comparison for different p>0. Our approach highlights the advantages of cluster inference based on extremal ℓα−blocks, where α>0 is the index of regular variation of the series. We focus on inference of important indices in extreme value theory, e.g., the extremal index.

KW - Cluster processes

KW - Extremal index

KW - Large deviation principles

KW - Regularly varying time series

U2 - 10.1016/j.spa.2023.03.013

DO - 10.1016/j.spa.2023.03.013

M3 - Journal article

AN - SCOPUS:85163650621

VL - 161

SP - 68

EP - 101

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

ER -

ID: 371273298

Institut for Matematiske Fag