Characterization of the tail behavior of a class of BEKK processes: A stochastic recurrence equation approach

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Standard

Characterization of the tail behavior of a class of BEKK processes: A stochastic recurrence equation approach. / Pedersen, Rasmus Søndergaard; Matsui, Muneya.

I: Econometric Theory, Bind 38, Nr. 1, 2022, s. 1-34.

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Harvard

Pedersen, RS & Matsui, M 2022, 'Characterization of the tail behavior of a class of BEKK processes: A stochastic recurrence equation approach', Econometric Theory, bind 38, nr. 1, s. 1-34. https://doi.org/10.1017/S0266466620000584

APA

Pedersen, R. S., & Matsui, M. (2022). Characterization of the tail behavior of a class of BEKK processes: A stochastic recurrence equation approach. Econometric Theory, 38(1), 1-34. https://doi.org/10.1017/S0266466620000584

Vancouver

Pedersen RS, Matsui M. Characterization of the tail behavior of a class of BEKK processes: A stochastic recurrence equation approach. Econometric Theory. 2022;38(1):1-34. https://doi.org/10.1017/S0266466620000584

Author

Pedersen, Rasmus Søndergaard ; Matsui, Muneya. / Characterization of the tail behavior of a class of BEKK processes: A stochastic recurrence equation approach. I: Econometric Theory. 2022 ; Bind 38, Nr. 1. s. 1-34.

Bibtex

@article{34d3a47f6d2141f2be3147327d93d079,
title = "Characterization of the tail behavior of a class of BEKK processes: A stochastic recurrence equation approach",
abstract = "We consider conditions for strict stationarity and ergodicity of a class of multivariate BEKK processes and study the tail behavior of the associated stationary distributions. Specifically, we consider a class of BEKK-ARCH processes where the innovations are assumed to be Gaussian and a finite number of lagged {\textquoteright}s may load into the conditional covariance matrix of . By exploiting that the processes have multivariate stochastic recurrence equation representations, we show the existence of strictly stationary solutions under mild conditions, where only a fractional moment of may be finite. Moreover, we show that each component of the BEKK processes is regularly varying with some tail index. In general, the tail index differs along the components, which contrasts with most of the existing literature on the tail behavior of multivariate GARCH processes. Lastly, in an empirical illustration of our theoretical results, we quantify the model-implied tail index of the daily returns on two cryptocurrencies.",
author = "Pedersen, {Rasmus S{\o}ndergaard} and Muneya Matsui",
year = "2022",
doi = "10.1017/S0266466620000584",
language = "English",
volume = "38",
pages = "1--34",
journal = "Econometric Theory",
issn = "0266-4666",
publisher = "Cambridge University Press",
number = "1",

}

RIS

TY - JOUR

T1 - Characterization of the tail behavior of a class of BEKK processes: A stochastic recurrence equation approach

AU - Pedersen, Rasmus Søndergaard

AU - Matsui, Muneya

PY - 2022

Y1 - 2022

N2 - We consider conditions for strict stationarity and ergodicity of a class of multivariate BEKK processes and study the tail behavior of the associated stationary distributions. Specifically, we consider a class of BEKK-ARCH processes where the innovations are assumed to be Gaussian and a finite number of lagged ’s may load into the conditional covariance matrix of . By exploiting that the processes have multivariate stochastic recurrence equation representations, we show the existence of strictly stationary solutions under mild conditions, where only a fractional moment of may be finite. Moreover, we show that each component of the BEKK processes is regularly varying with some tail index. In general, the tail index differs along the components, which contrasts with most of the existing literature on the tail behavior of multivariate GARCH processes. Lastly, in an empirical illustration of our theoretical results, we quantify the model-implied tail index of the daily returns on two cryptocurrencies.

AB - We consider conditions for strict stationarity and ergodicity of a class of multivariate BEKK processes and study the tail behavior of the associated stationary distributions. Specifically, we consider a class of BEKK-ARCH processes where the innovations are assumed to be Gaussian and a finite number of lagged ’s may load into the conditional covariance matrix of . By exploiting that the processes have multivariate stochastic recurrence equation representations, we show the existence of strictly stationary solutions under mild conditions, where only a fractional moment of may be finite. Moreover, we show that each component of the BEKK processes is regularly varying with some tail index. In general, the tail index differs along the components, which contrasts with most of the existing literature on the tail behavior of multivariate GARCH processes. Lastly, in an empirical illustration of our theoretical results, we quantify the model-implied tail index of the daily returns on two cryptocurrencies.

U2 - 10.1017/S0266466620000584

DO - 10.1017/S0266466620000584

M3 - Journal article

VL - 38

SP - 1

EP - 34

JO - Econometric Theory

JF - Econometric Theory

SN - 0266-4666

IS - 1

ER -

ID: 255114439