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

Abstract

The weighted least absolute deviations estimator is studied for an AR (1) process with ARCH (1) errors ε t . Unlike for the quasi maximum likelihood estimator, the estimator's, limiting distribution is shown to be normal even when E ( ε t 4 ) = ∞. Furthermore, the estimator can be applied to examine the symmetry of the density of ε t and to estimate the quantity E (log |α + λ ½ ε t |), which are of crucial importance for conducting asymptotic inference for quasi maximum likelihood estimators and weighted least absolute deviations estimators.