ASYMPTOTIC NORMALITY OF THE QUASI-MAXIMUM LIKELIHOOD ESTIMATOR FOR MULTIDIMENSIONAL CAUSAL PROCESSES

• 成果类型: Article
• 署名作者: Bardet, Jean-Marc; Wintenberger, Olivier
• 署名单位: heSam Universite; Universite Pantheon-Sorbonne
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS674
• 发表日期: 2009
• 页码: 2730-2759
• 关键词: arch models; garch processes; Consistency; volatility

摘要

Strong consistency and asymptotic normality of the quasi-maximum likelihood estimator are given for a general class of multidimensional causal processes. For particular cases already studied in the literature [for instance univariate or multivariate ARCH(infinity) processes], the assumptions required for establishing these results are often weaker than existing conditions. The QMLE asymptotic behavior is also given for numerous new examples of univariate or multivariate processes (for instance TARCH or NLARCH processes).