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

Claudia Klüppelberg, Serguei Peroamenchtchikov

Research output: Contribution to journalArticlepeer-review

43 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)971-1005
Number of pages35
JournalAnnals of Applied Probability
Volume14
Issue number2
DOIs
StatePublished - May 2004

Keywords

  • ARCH model
  • Autoregressive model
  • Geometric ergodicity
  • Heteroscedastic model
  • Random coefficient autoregressive process
  • Random recurrence equation
  • Regular variation
  • Renewal theorem for Markov chains
  • Strong mixing

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