On convergence of LAD estimates in autoregression with infinite variance

The least absolute deviation estimates L(N), from N data points, of the autoregressive constants a = (a₁, …, a_q)′ for a stationary autoregressive model, are shown to have the property that N^σ(L(N) ? a) converge to zero in probability, for $\text{σ <}\text{1}\text{α}$, where the disturbances are i.i.d., attracted to a stable law of index α, 1 ≤ α < 2, and satisfy some other conditions.