文章基本信息

标题：An extension of max autoregressive models
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作者：Philippe Naveau ; Zhengjun Zhang ; Bin Zhu 等
期刊名称：Statistics and Its Interface
印刷版ISSN：1938-7989
电子版ISSN：1938-7997
出版年度：2011
卷号：4
期号：2
页码：253-266
DOI：10.4310/SII.2011.v4.n2.a19
出版社：International Press
摘要：To model clustered maxima behaviors in time series analysis, max-autoregressive (MAR) and moving maxima (MM) processes are naturally adapted from linear autoregressive (AR) and moving average (MA) models. Yet, applications of MAR and MM processes are still sparse due to some difficulties of parameter inference and some abnormality of the processes. Basically, some ratios of observations can take constant values in MAR models. The objective of this present work is to introduce a new model that is closely related to the MAR processes and is free of the aforementioned abnormality. A logarithm transformation of the new model leads to time series models with log-positive alpha stable noises and hidden max Gumbel shocks. Theoretical properties of the new models are derived.
关键词：extreme value theory; dependence; Gumbel distribution; autoregressive model