On the Invertibility of EGARCH(p,q)

Of the two most widely estimated univariate asymmetric conditional volatility models, the exponential GARCH (or EGARCH) specification can capture asymmetry, which refers to the different effects on conditional volatility of positive and negative effects of equal magnitude, and leverage, which refers...

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Detalles Bibliográficos
Autores: Martinet, Guillaume Gaetan, McAleer, Michael
Tipo de recurso: informe técnico
Fecha de publicación:2015
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/41626
Acceso en línea:https://hdl.handle.net/20.500.14352/41626
Access Level:acceso abierto
Palabra clave:C22
C52
C58
G32
Leverage
Asymmetry
Existence
Stochastic process
Asymptotic properties
Invertibility.
Econometría (Economía)
5302 Econometría
id ES_78e2c4263de96bc3daa531d82cd635ff
oai_identifier_str oai:docta.ucm.es:20.500.14352/41626
network_acronym_str ES
network_name_str España
repository_id_str
spelling On the Invertibility of EGARCH(p,q)Martinet, Guillaume GaetanMcAleer, MichaelC22C52C58G32LeverageAsymmetryExistenceStochastic processAsymptotic propertiesInvertibility.Econometría (Economía)5302 EconometríaOf the two most widely estimated univariate asymmetric conditional volatility models, the exponential GARCH (or EGARCH) specification can capture asymmetry, which refers to the different effects on conditional volatility of positive and negative effects of equal magnitude, and leverage, which refers to the negative correlation between the returns shocks and subsequent shocks to volatility. However, the statistical properties of the (quasi-) maximum likelihood estimator (QMLE) of the EGARCH parameters are not available under general conditions, but only for special cases under highly restrictive and unverifiable conditions, such as EGARCH(1,0) or EGARCH(1,1), and possibly only under simulation. A limitation in the development of asymptotic properties of the QMLE for the EGARCH(p,q) model is the lack of an invertibility condition for the returns shocks underlying the model. It is shown in this paper that the EGARCH(p,q) model can be derived from a stochastic process, for which the invertibility conditions can be stated simply and explicitly. This will be useful in re-interpreting the existing properties of the QMLE of the EGARCH(p,q) parameters.Universidad Complutense de Madrid20152015-01-0120152015-01-01technical reporthttp://purl.org/coar/resource_type/c_18ghinfo:eu-repo/semantics/reportapplication/pdfhttps://hdl.handle.net/20.500.14352/41626reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Atribución-NoComercial-CompartirIgual 3.0 Españahttps://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/416262026-06-02T12:44:21Z
dc.title.none.fl_str_mv On the Invertibility of EGARCH(p,q)
title On the Invertibility of EGARCH(p,q)
spellingShingle On the Invertibility of EGARCH(p,q)
Martinet, Guillaume Gaetan
C22
C52
C58
G32
Leverage
Asymmetry
Existence
Stochastic process
Asymptotic properties
Invertibility.
Econometría (Economía)
5302 Econometría
title_short On the Invertibility of EGARCH(p,q)
title_full On the Invertibility of EGARCH(p,q)
title_fullStr On the Invertibility of EGARCH(p,q)
title_full_unstemmed On the Invertibility of EGARCH(p,q)
title_sort On the Invertibility of EGARCH(p,q)
dc.creator.none.fl_str_mv Martinet, Guillaume Gaetan
McAleer, Michael
author Martinet, Guillaume Gaetan
author_facet Martinet, Guillaume Gaetan
McAleer, Michael
author_role author
author2 McAleer, Michael
author2_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv C22
C52
C58
G32
Leverage
Asymmetry
Existence
Stochastic process
Asymptotic properties
Invertibility.
Econometría (Economía)
5302 Econometría
topic C22
C52
C58
G32
Leverage
Asymmetry
Existence
Stochastic process
Asymptotic properties
Invertibility.
Econometría (Economía)
5302 Econometría
description Of the two most widely estimated univariate asymmetric conditional volatility models, the exponential GARCH (or EGARCH) specification can capture asymmetry, which refers to the different effects on conditional volatility of positive and negative effects of equal magnitude, and leverage, which refers to the negative correlation between the returns shocks and subsequent shocks to volatility. However, the statistical properties of the (quasi-) maximum likelihood estimator (QMLE) of the EGARCH parameters are not available under general conditions, but only for special cases under highly restrictive and unverifiable conditions, such as EGARCH(1,0) or EGARCH(1,1), and possibly only under simulation. A limitation in the development of asymptotic properties of the QMLE for the EGARCH(p,q) model is the lack of an invertibility condition for the returns shocks underlying the model. It is shown in this paper that the EGARCH(p,q) model can be derived from a stochastic process, for which the invertibility conditions can be stated simply and explicitly. This will be useful in re-interpreting the existing properties of the QMLE of the EGARCH(p,q) parameters.
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-01-01
2015
2015-01-01
dc.type.none.fl_str_mv technical report
http://purl.org/coar/resource_type/c_18gh
dc.type.openaire.fl_str_mv info:eu-repo/semantics/report
format report
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/41626
url https://hdl.handle.net/20.500.14352/41626
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Atribución-NoComercial-CompartirIgual 3.0 España
https://creativecommons.org/licenses/by-nc-sa/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Atribución-NoComercial-CompartirIgual 3.0 España
https://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.81155

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