On tail behaviour of nonlinear autoregressive functional conditional heteroscedastic model with heavy-tailed innovations

J. Pan, G. Wu

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We study the tail probability of the stationary distribution of nonparametric nonlinear autoregressive functional conditional heteroscedastic (NARFCH) model with heavy-tailed innovations. Our result shows that the tail of the stationary marginal distribution of an NARFCH series is heavily dependent on its conditional variance. When the innovations are heavy-tailed, the tail of the stationary marginal distribution of the series will become heavier or thinner than that of its innovations. We give some specific formulas to show how the increment or decrement of tail heaviness depends on the assumption on the conditional variance function. Some examples are given.
Original languageEnglish
Pages (from-to)1169-1181
Number of pages12
JournalScience China Mathematics
Volume48
Issue number9
DOIs
Publication statusPublished - 2005

Keywords

  • tail probability
  • stationary distribution
  • nonlinear AR model
  • heavy-tailed distribution
  • statistics

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