Abstract: | The maximum likelihood estimate (MLE) of the autoregressive coefficient of a near‐unit root autoregressive process Yt = ρnYt?1 + ?t with α‐stable noise {?t} is studied in this paper. Herein ρn = 1 ? γ/n, γ ≥ 0 is a constant, Y0 is a fixed random variable and εt is an α‐stable random variable with characteristic function φ(t,θ) for some parameter θ. It is shown that when 0 < α < 1 or α > 1 and E?1 = 0, the limit distribution of the MLE of ρn and θ are mixtures of a stable process and Gaussian processes. On the other hand, when α > 1 and E?1 ≠ 0, the limit distribution of the MLE of ρn and θ are normal. A Monte Carlo simulation reveals that the MLE performs better than the usual least squares procedures, particularly for the case when the tail index α is less than 1. |