Least absolute deviation estimates in autoregression with infinite variance

We consider an L_1 analogue of the least squares estimate or for the parameters of stationary, finite order auto regressions. This estimator, the least absolute deviation (LAD), is shown to be strongly consistent via a result that may have independent interest. The striking feature is that the conditions are so mild as to include processes with infinite variance, notably the stationary, finite auto regressions driven by stable increments in L_alpha, alpha>l. Finally sampling properties of LAD are compared to those of least squares. Together with a known convergence rate result for least squares, the Monte-Carlo study provides evidence for a conjecture on the convergence rate of LAD.Technical report DCS-TR-6