Robust and efficient estimation of GARCH models based on Hellinger distance
© 2021 Informa UK Limited, trading as Taylor & Francis Group.
| Veröffentlicht in: | Journal of applied statistics. - 1991. - 49(2022), 15 vom: 11., Seite 3976-4002 |
|---|---|
| 1. Verfasser: | |
| Weitere Verfasser: | , |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2022
|
| Zugriff auf das übergeordnete Werk: | Journal of applied statistics |
| Schlagworte: | Journal Article 62G05 62G35 GARCH models Primary 62F10 kernel estimation maximum likelihood estimation minimum (profile) Hellinger distance estimation robustness secondary 62G07 |
| Zusammenfassung: | © 2021 Informa UK Limited, trading as Taylor & Francis Group. It is well known that financial data frequently contain outlying observations. Almost all methods and techniques used to estimate GARCH models are likelihood-based and thus generally non-robust against outliers. Minimum distance method, as an important tool for statistical inferences and a competitive alternative for achieving robustness, has surprisingly not been well explored for GARCH models. In this paper, we proposed a minimum Hellinger distance estimator (MHDE) and a minimum profile Hellinger distance estimator (MPHDE), depending on whether the innovation distribution is specified or not, for estimating the parameters in GARCH models. The construction and investigation of the two estimators are quite involved due to the non-i.i.d. nature of data. We proved that the MHDE is a consistent estimator and derived its bias in explicit expression. For both of the proposed estimators, we demonstrated their finite-sample performance through simulation studies and compared with the well-established methods including MLE, Gaussian Quasi-MLE, Non-Gaussian Quasi-MLE and Least Absolute Deviation estimator. Our numerical results showed that MHDE and MPHDE have much better performance than MLE-based methods when data are contaminated while simultaneously they are very competitive when data is clean, which testified to the robustness and efficiency of the two proposed MHD-type estimations |
|---|---|
| Beschreibung: | Date Revised 03.11.2022 published: Electronic-eCollection Citation Status PubMed-not-MEDLINE |
| ISSN: | 0266-4763 |
| DOI: | 10.1080/02664763.2021.1970120 |