GLOBAL SELF-WEIGHTED AND LOCAL QUASI-MAXIMUM EXPONENTIAL LIKELIHOOD ESTIMATORS FOR ARMA-GARCH/IGARCH MODELS

• 成果类型: Article
• 署名作者: Zhu, Ke; Ling, Shiqing
• 署名单位: Hong Kong University of Science & Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS895
• 发表日期: 2011
• 页码: 2131-2163
• 关键词: absolute deviation estimation; time-series models; garch processes; CONDITIONAL HETEROSCEDASTICITY; infinite variance; ASYMPTOTIC THEORY; ARCH; errors; regression

摘要

This paper investigates the asymptotic theory of the quasi-maximum exponential likelihood estimators (QMELE) for ARMA-GARCH models. Under only a fractional moment condition, the strong consistency and the asymptotic normality of the global self-weighted QMELE are obtained. Based on this self-weighted QMELE, the local QMELE is showed to be asymptotically normal for the ARMA model with GARCH (finite variance) and IGARCH errors. A formal comparison of two estimators is given for some cases. A simulation study is carried out to assess the performance of these estimators, and a real example on the world crude oil price is given.