Stable limits for sums of dependent infinite variance random variables

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Standard

Stable limits for sums of dependent infinite variance random variables. / Bartkiewicz, Katarszyna; Jakubowski, Adam ; Mikosch, Thomas Valentin; Wintenberger, Olivier .

I: Probability Theory and Related Fields, Bind 150, Nr. 3-4, 2011, s. 337-372.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Bartkiewicz, K, Jakubowski, A, Mikosch, TV & Wintenberger, O 2011, 'Stable limits for sums of dependent infinite variance random variables', Probability Theory and Related Fields, bind 150, nr. 3-4, s. 337-372. https://doi.org/10.1007/s00440-010-0276-9

APA

Bartkiewicz, K., Jakubowski, A., Mikosch, T. V., & Wintenberger, O. (2011). Stable limits for sums of dependent infinite variance random variables. Probability Theory and Related Fields, 150(3-4), 337-372. https://doi.org/10.1007/s00440-010-0276-9

Vancouver

Bartkiewicz K, Jakubowski A, Mikosch TV, Wintenberger O. Stable limits for sums of dependent infinite variance random variables. Probability Theory and Related Fields. 2011;150(3-4): 337-372. https://doi.org/10.1007/s00440-010-0276-9

Author

Bartkiewicz, Katarszyna ; Jakubowski, Adam ; Mikosch, Thomas Valentin ; Wintenberger, Olivier . / Stable limits for sums of dependent infinite variance random variables. I: Probability Theory and Related Fields. 2011 ; Bind 150, Nr. 3-4. s. 337-372.

Bibtex

@article{2b8c9ba99a264a0f97ae531ddcb7571d,
title = "Stable limits for sums of dependent infinite variance random variables",
abstract = "The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to hold are known in the literature. However, most of these results are qualitative in the sense that the parameters of the limit distribution are expressed in terms of some limiting point process. In this paper we will be able to determine the parameters of the limiting stable distribution in terms of some tail characteristics of the underlying stationary sequence. We will apply our results to some standard time series models, including the GARCH(1, 1) process and its squares, the stochastic volatility models and solutions to stochastic recurrence equations.",
keywords = "Stationary sequence, Stable limit distribution, Weak convergence, Mixing, Weak dependence, Characteristic function, Regular variation, GARCH, Stochastic volatility model, ARMA process",
author = "Katarszyna Bartkiewicz and Adam Jakubowski and Mikosch, {Thomas Valentin} and Olivier Wintenberger",
year = "2011",
doi = "10.1007/s00440-010-0276-9",
language = "English",
volume = "150",
pages = " 337--372",
journal = "Probability Theory and Related Fields",
issn = "0178-8051",
publisher = "Springer",
number = "3-4",

}

RIS

TY - JOUR

T1 - Stable limits for sums of dependent infinite variance random variables

AU - Bartkiewicz, Katarszyna

AU - Jakubowski, Adam

AU - Mikosch, Thomas Valentin

AU - Wintenberger, Olivier

PY - 2011

Y1 - 2011

N2 - The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to hold are known in the literature. However, most of these results are qualitative in the sense that the parameters of the limit distribution are expressed in terms of some limiting point process. In this paper we will be able to determine the parameters of the limiting stable distribution in terms of some tail characteristics of the underlying stationary sequence. We will apply our results to some standard time series models, including the GARCH(1, 1) process and its squares, the stochastic volatility models and solutions to stochastic recurrence equations.

AB - The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to hold are known in the literature. However, most of these results are qualitative in the sense that the parameters of the limit distribution are expressed in terms of some limiting point process. In this paper we will be able to determine the parameters of the limiting stable distribution in terms of some tail characteristics of the underlying stationary sequence. We will apply our results to some standard time series models, including the GARCH(1, 1) process and its squares, the stochastic volatility models and solutions to stochastic recurrence equations.

KW - Stationary sequence

KW - Stable limit distribution

KW - Weak convergence

KW - Mixing

KW - Weak dependence

KW - Characteristic function

KW - Regular variation

KW - GARCH

KW - Stochastic volatility model

KW - ARMA process

U2 - 10.1007/s00440-010-0276-9

DO - 10.1007/s00440-010-0276-9

M3 - Journal article

VL - 150

SP - 337

EP - 372

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 3-4

ER -

ID: 36006265