LEAST ABSOLUTE DEVIATION ESTIMATES IN AUTOREGRESSION WITH INFINITE VARIANCE

An L//1 analog of the least squares estimator for the parameters of stationary, finite-order autoregressions is considered. 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 autoregressions driven by stable increments in L// alpha , alpha greater than 1. 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.