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Limit theory and robust evaluation methods for the extremal properties of GARCH(p, q) processes

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Limit theory and robust evaluation methods for the extremal properties of GARCH(p, q) processes. / Laurini, Fabrizio; Fearnhead, Paul; Tawn, Jonathan.
In: Statistics and Computing, Vol. 32, No. 6, 01.11.2022.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Laurini, F, Fearnhead, P & Tawn, J 2022, 'Limit theory and robust evaluation methods for the extremal properties of GARCH(p, q) processes', Statistics and Computing, vol. 32, no. 6. https://doi.org/10.1007/s11222-022-10164-5

APA

Laurini, F., Fearnhead, P., & Tawn, J. (2022). Limit theory and robust evaluation methods for the extremal properties of GARCH(p, q) processes. Statistics and Computing, 32(6). Advance online publication. https://doi.org/10.1007/s11222-022-10164-5

Vancouver

Laurini F, Fearnhead P, Tawn J. Limit theory and robust evaluation methods for the extremal properties of GARCH(p, q) processes. Statistics and Computing. 2022 Nov 1;32(6). Epub 2022 Nov 1. doi: 10.1007/s11222-022-10164-5

Author

Laurini, Fabrizio ; Fearnhead, Paul ; Tawn, Jonathan. / Limit theory and robust evaluation methods for the extremal properties of GARCH(p, q) processes. In: Statistics and Computing. 2022 ; Vol. 32, No. 6.

Bibtex

@article{6335cd11ea19438695faba4d598e2dc0,
title = "Limit theory and robust evaluation methods for the extremal properties of GARCH(p, q) processes",
abstract = "Generalized autoregressive conditionally heteroskedastic (GARCH) processes are widely used for modelling financial returns, with their extremal properties being of interest for market risk management. For GARCH(p,q) processes with max(p,q) = 1 all extremal features have been fully characterised, but when max(p,q) is greater than or equal to 2 much remains to be found. Previous research has identified that both marginal and dependence extremal features of strictly stationary GARCH(p,q) processes are determined by a multivariate regular variation property and tail processes. Currently there are no reliable methods for evaluating these characterisations, or even assessing the stationarity, for the classes of GARCH(p,q) processes that are used in practice, i.e., with unbounded and asymmetric innovations. By developing a mixture of new limit theory and particle filtering algorithms for fixed point distributions we produce novel and robust evaluation methods for all extremal features for all GARCH(p,q) processes, including ARCH and IGARCH processes. We investigate our methods' performance when evaluating the marginal tail index, the extremogram and the extremal index, the latter two being measures of temporal dependence. ",
author = "Fabrizio Laurini and Paul Fearnhead and Jonathan Tawn",
year = "2022",
month = nov,
day = "1",
doi = "10.1007/s11222-022-10164-5",
language = "English",
volume = "32",
journal = "Statistics and Computing",
issn = "0960-3174",
publisher = "Springer Netherlands",
number = "6",

}

RIS

TY - JOUR

T1 - Limit theory and robust evaluation methods for the extremal properties of GARCH(p, q) processes

AU - Laurini, Fabrizio

AU - Fearnhead, Paul

AU - Tawn, Jonathan

PY - 2022/11/1

Y1 - 2022/11/1

N2 - Generalized autoregressive conditionally heteroskedastic (GARCH) processes are widely used for modelling financial returns, with their extremal properties being of interest for market risk management. For GARCH(p,q) processes with max(p,q) = 1 all extremal features have been fully characterised, but when max(p,q) is greater than or equal to 2 much remains to be found. Previous research has identified that both marginal and dependence extremal features of strictly stationary GARCH(p,q) processes are determined by a multivariate regular variation property and tail processes. Currently there are no reliable methods for evaluating these characterisations, or even assessing the stationarity, for the classes of GARCH(p,q) processes that are used in practice, i.e., with unbounded and asymmetric innovations. By developing a mixture of new limit theory and particle filtering algorithms for fixed point distributions we produce novel and robust evaluation methods for all extremal features for all GARCH(p,q) processes, including ARCH and IGARCH processes. We investigate our methods' performance when evaluating the marginal tail index, the extremogram and the extremal index, the latter two being measures of temporal dependence.

AB - Generalized autoregressive conditionally heteroskedastic (GARCH) processes are widely used for modelling financial returns, with their extremal properties being of interest for market risk management. For GARCH(p,q) processes with max(p,q) = 1 all extremal features have been fully characterised, but when max(p,q) is greater than or equal to 2 much remains to be found. Previous research has identified that both marginal and dependence extremal features of strictly stationary GARCH(p,q) processes are determined by a multivariate regular variation property and tail processes. Currently there are no reliable methods for evaluating these characterisations, or even assessing the stationarity, for the classes of GARCH(p,q) processes that are used in practice, i.e., with unbounded and asymmetric innovations. By developing a mixture of new limit theory and particle filtering algorithms for fixed point distributions we produce novel and robust evaluation methods for all extremal features for all GARCH(p,q) processes, including ARCH and IGARCH processes. We investigate our methods' performance when evaluating the marginal tail index, the extremogram and the extremal index, the latter two being measures of temporal dependence.

U2 - 10.1007/s11222-022-10164-5

DO - 10.1007/s11222-022-10164-5

M3 - Journal article

VL - 32

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

IS - 6

ER -