Geometric ergodicity and conditional self-weighted M-estimator of a GRCAR(p) model with heavy‐tailed errors

Xiaoyan Li, Jiazhu Pan, Anchao Song

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Abstract

We establish the geometric ergodicity for general stochastic functional autoregressive (linear and nonlinear) models with heavy-tailed errors. The stationarity conditions for a generalized random coefficient autoregressive model (GRCAR($p$)) are presented as a corollary. And then, a conditional self-weighted M-estimator for parameters in the GRCAR($p$) is proposed. The asymptotic normality of this estimator is discussed by allowing infinite variance innovations. Simulation experiments are carried out to assess the finite-sample performance of the proposed methodology and theory, and a real heavy-tailed data example is given as illustration.
Original languageEnglish
Pages (from-to)418-436
Number of pages19
JournalJournal of Time Series Analysis
Volume44
Issue number4
Early online date19 Jan 2023
DOIs
Publication statusPublished - 31 Jul 2023

Keywords

  • stochastic functional autoregression
  • generalized random coefficient autoregressive model
  • geometric ergodicity
  • self-weighted M-estimator
  • asymptotic normality

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