Limit Theory for Stationary Autoregression with Heavy-Tailed Augmented GARCH Innovations
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Hwang, Eunju | - |
dc.date.accessioned | 2021-05-10T07:40:02Z | - |
dc.date.available | 2021-05-10T07:40:02Z | - |
dc.date.created | 2021-05-06 | - |
dc.date.issued | 2021-04 | - |
dc.identifier.issn | 2227-7390 | - |
dc.identifier.uri | https://scholarworks.bwise.kr/gachon/handle/2020.sw.gachon/80965 | - |
dc.description.abstract | This paper considers stationary autoregressive (AR) models with heavy-tailed, general GARCH (G-GARCH) or augmented GARCH noises. Limit theory for the least squares estimator (LSE) of autoregression coefficient ρ = ρn is derived uniformly over stationary values in [0, 1), focusing on ρn → 1 as sample size n tends to infinity. For tail index α ε (0, 4) of G-GARCH innovations, asymptotic distributions of the LSEs are established, which are involved with the stable distribution. The convergence rate of the LSE depends on 1 - ρ2 n, but no condition on the rate of ρn is required. It is shown that, for the tail index α ε (0, 2), the LSE is inconsistent, for α = 2, log n/(1 - ρ2 n)- consistent, and for α ε (2, 4), n1-2/α/(1 - ρ2 n)-consistent. Proofs are based on the point process and the asymptotic properties in AR models with G-GARCH errors. However, this present work provides a bridge between pure stationary and unit-root processes. This paper extends the existing uniform limit theory with three issues: the errors have conditional heteroscedastic variance; the errors are heavy-tailed with tail index α ε (0, 4); and no restriction on the rate of ρn is necessary. © 2021 by the authors. Licensee MDPI, Basel, Switzerland. | - |
dc.language | 영어 | - |
dc.language.iso | en | - |
dc.publisher | MDPI | - |
dc.relation.isPartOf | Mathematics | - |
dc.title | Limit Theory for Stationary Autoregression with Heavy-Tailed Augmented GARCH Innovations | - |
dc.type | Article | - |
dc.type.rims | ART | - |
dc.description.journalClass | 1 | - |
dc.identifier.wosid | 000644523700001 | - |
dc.identifier.doi | 10.3390/math9080816 | - |
dc.identifier.bibliographicCitation | Mathematics, v.9, no.8 | - |
dc.description.isOpenAccess | N | - |
dc.identifier.scopusid | 2-s2.0-85104839988 | - |
dc.citation.title | Mathematics | - |
dc.citation.volume | 9 | - |
dc.citation.number | 8 | - |
dc.contributor.affiliatedAuthor | Hwang, Eunju | - |
dc.type.docType | Article | - |
dc.subject.keywordAuthor | Augmented GARCH | - |
dc.subject.keywordAuthor | Autoregression | - |
dc.subject.keywordAuthor | Heavy-tailed | - |
dc.subject.keywordAuthor | Limit theory | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.
1342, Seongnam-daero, Sujeong-gu, Seongnam-si, Gyeonggi-do, Republic of Korea(13120)031-750-5114
COPYRIGHT 2020 Gachon University All Rights Reserved.
Certain data included herein are derived from the © Web of Science of Clarivate Analytics. All rights reserved.
You may not copy or re-distribute this material in whole or in part without the prior written consent of Clarivate Analytics.