Weighted least absolute deviations estimation for ARFIMA time series with finite or infinite variance

In this paper a weighted least absolute deviations (WLAD) estimator for fractionally autoregressive integrated moving average (ARFIMA) models is proposed, in which stationary and non-stationary cases are discussed. The asymptotic normality of their local estimators is derived under a fractional moment condition. A Wald test for a linear hypothesis has been constructed, its limiting distribution is presented, and a simulation study is given to evaluate the performance of the proposed WLAD estimator under the stationary case.