Asymptotic inference of least absolute deviation estimation for AR(1) processes

In this article, we consider a first-order autoregressive process y(t) = rho(n)y(t-1) + u(t) with n vertical bar 1-rho(n)vertical bar -> infinity as n -> infinity. The Gaussian limit theory and the Cauchy limit theory of the least absolute deviation estimator for the near-stationary process (rho(n) is an element of [0; 1)) and the mildly explosive process (rho(n)>1) are derived, respectively. The results are complementary to the uniform limit theory of least squares estimators for stationary autoregressions in Giraitis and Phillips (2006). Some simulations are carried out to assess the performance of our procedure.