WEAK CONVERGENCE OF A PSEUDO MAXIMUM LIKELIHOOD ESTIMATOR FOR THE EXTREMAL INDEX

• 成果类型: Article
• 署名作者: Berghaus, Betina; Buecher, Axel
• 署名单位: Ruhr University Bochum
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/17-AOS1621
• 发表日期: 2018
• 页码: 2307-2335
• 关键词: stochastic difference equation; stationary sequence; random-variables; VALUES; inference; BEHAVIOR; blocks

摘要

The extremes of a stationary time series typically occur in clusters. A primary measure for this phenomenon is the extremal index, representing the reciprocal of the expected cluster size. Both disjoint and sliding blocks estimator for the extremal index are analyzed in detail. In contrast to many competitors, the estimators only depend on the choice of one parameter sequence. We derive an asymptotic expansion, prove asymptotic normality and show consistency of an estimator for the asymptotic variance. Explicit calculations in certain models and a finite-sample Monte Carlo simulation study reveal that the sliding blocks estimator outperforms other blocks estimators, and that it is competitive to runs- and inter-exceedance estimators in various models. The methods are applied to a variety of financial time series.