  This paper provides an entire inference procedure for the autoregressive
model under (conditional) heteroscedasticity of unknown form with a finite
variance. We first establish the asymptotic normality of the weighted least
absolute deviations estimator (LADE) for the model. Second, we develop the
random weighting (RW) method to estimate its asymptotic covariance matrix,
leading to the implementation of the Wald test. Third, we construct a
portmanteau test for model checking, and use the RW method to obtain its
critical values. As a special weighted LADE, the feasible adaptive LADE (ALADE)
is proposed and proved to have the same efficiency as its infeasible
counterpart. The importance of our entire methodology based on the feasible
ALADE is illustrated by simulation results and the real data analysis on three
U.S. economic data sets.
