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

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()) are presented as a corollary. And then, a conditional self‐weighted M‐estimator for parameters in the GRCAR() 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.