AbstractWe consider an L_1 analogue of the least squares estimator for the parameters of a stationary, finite order autoregressive scheme based on stable random variables. This estimator, the least absolute deviation (LAD), is shown to be strongly consistent via a result that may have independent interest. Finally, the sampling properties are compared to those of least squares. Together with a known convergence rate result for least squares, this provides evidence for a conjecture concerning the rate of convergence of LAD estimators.
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