Asymptotic Properties of the M-estimation for an AR(1) Process with a General Autoregressive Coefficient

摘要

In this paper, we consider a first-order autoregressive process with a general autoregressive coefficient. Asymptotic behaviors of an M-estimator of the autoregressive coefficient are established for the nearly stationary and mildly explosive cases, respectively. The rate of convergence of the robust estimators for the two cases are provided. The results extend ones for the least squares and least absolute deviation estimators to the robust estimator under the weaker initial conditions in the literature. Some simulations are carried out to assess the performance of our procedure.

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