Truncated sum-of-squares estimation of fractional time series models with generalized power law trend

We consider truncated (or conditional) sum-of-squares estimation of a parametric fractional time series model with an additive deterministic structure. The latter consists of both a drift term and a generalized power law trend. The memory parameter of the stochastic component and the power parameter...

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Detalhes bibliográficos
Autores: Hualde Bilbao, Javier, Nielsen, Morten Ørregaard
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:España
Recursos:Universidad Pública de Navarra
Repositorio:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
OAI Identifier:oai:academica-e.unavarra.es:2454/43702
Acesso em linha:https://hdl.handle.net/2454/43702
Access Level:acceso abierto
Palavra-chave:Asymptotic normality
Consistency
Deterministic trend
Fractional process
Generalized polynomial trend
Generalized power law trend
Noninvertibility
Nonstationarity
Sum-of-squares estimation
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spelling Truncated sum-of-squares estimation of fractional time series models with generalized power law trendHualde Bilbao, JavierNielsen, Morten ØrregaardAsymptotic normalityConsistencyDeterministic trendFractional processGeneralized polynomial trendGeneralized power law trendNoninvertibilityNonstationaritySum-of-squares estimationWe consider truncated (or conditional) sum-of-squares estimation of a parametric fractional time series model with an additive deterministic structure. The latter consists of both a drift term and a generalized power law trend. The memory parameter of the stochastic component and the power parameter of the deterministic trend component are both considered unknown real numbers to be estimated and belonging to arbitrarily large compact sets. Thus, our model captures different forms of nonstationarity and noninvertibility as well as a very flexible deterministic specification. As in related settings, the proof of consistency (which is a prerequisite for proving asymptotic normality) is challenging due to non-uniform convergence of the objective function over a large admissible parameter space and due to the competition between stochastic and deterministic components. As expected, parameter estimates related to the deterministic component are shown to be consistent and asymptotically normal only for parts of the parameter space depending on the relative strength of the stochastic and deterministic components. In contrast, we establish consistency and asymptotic normality of parameter estimates related to the stochastic component for the entire parameter space. Furthermore, the asymptotic distribution of the latter estimates is unaffected by the presence of the deterministic component, even when this is not consistently estimable. We also include Monte Carlo simulations to illustrate our results.J. Hualde's research is supported by the Spanish Ministerio de Ciencia e Innovación through project PGC2018-093542-B-I00.Institute of Mathematical StatisticsEconomíaEkonomia2022info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2454/43702reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarrainstname:Universidad Pública de NavarraInglésinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-093542-B-I00Creative Commons Attribution 4.0 International Licensehttps://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:academica-e.unavarra.es:2454/437022026-06-17T12:41:47Z
dc.title.none.fl_str_mv Truncated sum-of-squares estimation of fractional time series models with generalized power law trend
title Truncated sum-of-squares estimation of fractional time series models with generalized power law trend
spellingShingle Truncated sum-of-squares estimation of fractional time series models with generalized power law trend
Hualde Bilbao, Javier
Asymptotic normality
Consistency
Deterministic trend
Fractional process
Generalized polynomial trend
Generalized power law trend
Noninvertibility
Nonstationarity
Sum-of-squares estimation
title_short Truncated sum-of-squares estimation of fractional time series models with generalized power law trend
title_full Truncated sum-of-squares estimation of fractional time series models with generalized power law trend
title_fullStr Truncated sum-of-squares estimation of fractional time series models with generalized power law trend
title_full_unstemmed Truncated sum-of-squares estimation of fractional time series models with generalized power law trend
title_sort Truncated sum-of-squares estimation of fractional time series models with generalized power law trend
dc.creator.none.fl_str_mv Hualde Bilbao, Javier
Nielsen, Morten Ørregaard
author Hualde Bilbao, Javier
author_facet Hualde Bilbao, Javier
Nielsen, Morten Ørregaard
author_role author
author2 Nielsen, Morten Ørregaard
author2_role author
dc.contributor.none.fl_str_mv Economía
Ekonomia
dc.subject.none.fl_str_mv Asymptotic normality
Consistency
Deterministic trend
Fractional process
Generalized polynomial trend
Generalized power law trend
Noninvertibility
Nonstationarity
Sum-of-squares estimation
topic Asymptotic normality
Consistency
Deterministic trend
Fractional process
Generalized polynomial trend
Generalized power law trend
Noninvertibility
Nonstationarity
Sum-of-squares estimation
description We consider truncated (or conditional) sum-of-squares estimation of a parametric fractional time series model with an additive deterministic structure. The latter consists of both a drift term and a generalized power law trend. The memory parameter of the stochastic component and the power parameter of the deterministic trend component are both considered unknown real numbers to be estimated and belonging to arbitrarily large compact sets. Thus, our model captures different forms of nonstationarity and noninvertibility as well as a very flexible deterministic specification. As in related settings, the proof of consistency (which is a prerequisite for proving asymptotic normality) is challenging due to non-uniform convergence of the objective function over a large admissible parameter space and due to the competition between stochastic and deterministic components. As expected, parameter estimates related to the deterministic component are shown to be consistent and asymptotically normal only for parts of the parameter space depending on the relative strength of the stochastic and deterministic components. In contrast, we establish consistency and asymptotic normality of parameter estimates related to the stochastic component for the entire parameter space. Furthermore, the asymptotic distribution of the latter estimates is unaffected by the presence of the deterministic component, even when this is not consistently estimable. We also include Monte Carlo simulations to illustrate our results.
publishDate 2022
dc.date.none.fl_str_mv 2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2454/43702
url https://hdl.handle.net/2454/43702
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-093542-B-I00
dc.rights.none.fl_str_mv Creative Commons Attribution 4.0 International License
https://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Creative Commons Attribution 4.0 International License
https://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Institute of Mathematical Statistics
publisher.none.fl_str_mv Institute of Mathematical Statistics
dc.source.none.fl_str_mv reponame:Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
instname:Universidad Pública de Navarra
instname_str Universidad Pública de Navarra
reponame_str Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
collection Academica-e. Repositorio Institucional de la Universidad Pública de Navarra
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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