Limit Theory for Stationary Autoregression with Heavy-Tailed Augmented GARCH Innovations
- Authors
- Hwang, Eunju
- Issue Date
- Apr-2021
- Publisher
- MDPI
- Keywords
- Augmented GARCH; Autoregression; Heavy-tailed; Limit theory
- Citation
- Mathematics, v.9, no.8
- Journal Title
- Mathematics
- Volume
- 9
- Number
- 8
- URI
- https://scholarworks.bwise.kr/gachon/handle/2020.sw.gachon/80965
- DOI
- 10.3390/math9080816
- ISSN
- 2227-7390
- 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.
- Files in This Item
- There are no files associated with this item.
- Appears in
Collections - 사회과학대학 > 응용통계학과 > 1. Journal Articles
![qrcode](https://api.qrserver.com/v1/create-qr-code/?size=55x55&data=https://scholarworks.bwise.kr/gachon/handle/2020.sw.gachon/80965)
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.