A large deviations approach to limit theory for heavy-tailed time series

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A large deviations approach to limit theory for heavy-tailed time series. / Mikosch, Thomas Valentin; Wintenberger, Olivier.

In: Probability Theory and Related Fields, Vol. 166, 2016, p. 233-269.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Mikosch, TV & Wintenberger, O 2016, 'A large deviations approach to limit theory for heavy-tailed time series', Probability Theory and Related Fields, vol. 166, pp. 233-269. https://doi.org/10.1007/s00440-015-0654-4

APA

Mikosch, T. V., & Wintenberger, O. (2016). A large deviations approach to limit theory for heavy-tailed time series. Probability Theory and Related Fields, 166, 233-269. https://doi.org/10.1007/s00440-015-0654-4

Vancouver

Mikosch TV, Wintenberger O. A large deviations approach to limit theory for heavy-tailed time series. Probability Theory and Related Fields. 2016;166:233-269. https://doi.org/10.1007/s00440-015-0654-4

Author

Mikosch, Thomas Valentin ; Wintenberger, Olivier. / A large deviations approach to limit theory for heavy-tailed time series. In: Probability Theory and Related Fields. 2016 ; Vol. 166. pp. 233-269.

Bibtex

@article{38c6de5b426b4a27b3cd0af09ba2487c,
title = "A large deviations approach to limit theory for heavy-tailed time series",
abstract = "In this paper we propagate a large deviations approach for proving limit theory for (generally) multivariate time series with heavy tails. We make this notion precise by introducing regularly varying time series. We provide general large deviation results for functionals acting on a sample path and vanishing in some neighborhood of the origin. We study a variety of such functionals, including large deviations of random walks, their suprema, the ruin functional, and further derive weak limit theory for maxima, point processes, cluster functionals and the tail empirical process. One of the main results of this paper concerns bounds for the ruin probability in various heavy-tailed models including GARCH, stochastic volatility models and solutions to stochastic recurrence equations.",
author = "Mikosch, {Thomas Valentin} and Olivier Wintenberger",
year = "2016",
doi = "10.1007/s00440-015-0654-4",
language = "English",
volume = "166",
pages = "233--269",
journal = "Probability Theory and Related Fields",
issn = "0178-8051",
publisher = "Springer",

}

RIS

TY - JOUR

T1 - A large deviations approach to limit theory for heavy-tailed time series

AU - Mikosch, Thomas Valentin

AU - Wintenberger, Olivier

PY - 2016

Y1 - 2016

N2 - In this paper we propagate a large deviations approach for proving limit theory for (generally) multivariate time series with heavy tails. We make this notion precise by introducing regularly varying time series. We provide general large deviation results for functionals acting on a sample path and vanishing in some neighborhood of the origin. We study a variety of such functionals, including large deviations of random walks, their suprema, the ruin functional, and further derive weak limit theory for maxima, point processes, cluster functionals and the tail empirical process. One of the main results of this paper concerns bounds for the ruin probability in various heavy-tailed models including GARCH, stochastic volatility models and solutions to stochastic recurrence equations.

AB - In this paper we propagate a large deviations approach for proving limit theory for (generally) multivariate time series with heavy tails. We make this notion precise by introducing regularly varying time series. We provide general large deviation results for functionals acting on a sample path and vanishing in some neighborhood of the origin. We study a variety of such functionals, including large deviations of random walks, their suprema, the ruin functional, and further derive weak limit theory for maxima, point processes, cluster functionals and the tail empirical process. One of the main results of this paper concerns bounds for the ruin probability in various heavy-tailed models including GARCH, stochastic volatility models and solutions to stochastic recurrence equations.

U2 - 10.1007/s00440-015-0654-4

DO - 10.1007/s00440-015-0654-4

M3 - Journal article

VL - 166

SP - 233

EP - 269

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

ER -

ID: 148693460