Asymptotics for the conditional self-weighted M-estimator of GRCA(1) models with possibly heavy-tailed errors

Abstract

Consider a generalized random coefficient AR(1) model, $$y_t=\Phi _t y_{t-1}+u_t$$ , where $$\{(\Phi _t, u_t)^\prime , t\ge 1\}$$ is a sequences of i.i.d. random vectors, and a conditional self-weighted M-estimator of $$\textsf {E}\Phi _t$$ is proposed. The asymptotically normality of this new estimator is established with $$\textsf {E}u_t^2$$ being possibly infinite. Simulation experiments are carried out to assess the performance of the theory and method in finite samples and a real data example is given.