The tail of the stationary distribution of a random coefficient Ar(q) model

• 成果类型: Article
• 署名作者: Klüppelberg, C; Pergamenchtchikov, S
• 署名单位: Technical University of Munich; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000189
• 发表日期: 2004
• 页码: 971-1005
• 关键词: renewal theory; markov-chain; STATE-SPACE; functionals

摘要

We investigate a stationary random coefficient autoregressive process. Using renewal type arguments tailor-made for such processes, we show that the stationary distribution has a power-law tail. When the model is normal, we show that the model is in distribution equivalent to an autoregressive process with ARCH errors. Hence, we obtain the tail behavior of any such model of arbitrary order.