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

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.