Autoregressive processes with infinite variance

Abstract

The least squares estimators β_i(N), j = 1, …, p, from N data points, of the autoregressive constants for a stationary autoregressive model are considered when the disturbances have a distribution attracted to a stable law of index α < 2. It is shown that N^1/δ(β_i(N) – β) converges almost surely to zero for any δ > α. Some comments are made on alternative definitions of the β_i(N).