The efficiency of the estimators of the parameters in GARCH processes

• 成果类型: Article
• 署名作者: Berkes, I; Horváth, L
• 署名单位: Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Utah System of Higher Education; University of Utah
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2004
• 页码: 633-655
• 关键词: MAXIMUM LIKELIHOOD ESTIMATOR; conditional heteroskedasticity; models; stationarity; Consistency

摘要

We propose a class of estimators for the parameters of a GARCH(p, q) sequence. We show that our estimators are consistent and asymptotically normal under mild conditions. The quasi-maximum likelihood and the likelihood estimators are discussed in detail. We show that the maximum likelihood estimator is optimal. If the tail of the distribution of the innovations is polynomial, even a quasi-maximum likelihood estimator based on exponential density performs better than the standard normal density-based quasi-likelihood estimator of Lee and Hansen and Lumsdaine.