Asymptotic theory for LAD estimation of moderate deviations from a unit root

An asymptotic result is given for the least absolute deviations (LAD) estimation of autoregressive time series with a root of the form ρn=1+c/kn, where kn increases to infinity at a rate slower than n. For c<0, a nkn rate of convergence and asymptotic normality for the serial correlation coefficient are provided. While in the case of c>0, the serial correlation coefficient is shown to have a Cauchy limit distribution with a knρnn convergence rate. The results are complementary to the limit theory of least squares (LS) estimator which has been established in Phillips and Magdalinos (2007a).