Weighted least absolute deviations estimation for an AR(1) process with ARCH(1) errors

The weighted least absolute deviations estimator is studied for an AR(1) process with ARCH(1) errors c, Unlike for the quasi maximum likelihood estimator, the estimator's limiting distribution is shown to be normal even when E(epsilon(4)(t)) = infinity. Furthermore, the estimator can be applied to examine the symmetry of the density of epsilon(t) and to estimate the quantity E(log vertical bar alpha + lambda(1/2)epsilon(t)vertical bar), which are of crucial importance for conducting asymptotic inference for quasi maximum likelihood estimators and weighted least absolute deviations estimators.