M-estimation of linear models with dependent errors

Abstract

We study asymptotic properties of M -estimates of regression parameters in linear models in which errors are dependent. Weak and strong Bahadur representations of the M -estimates are derived and a central limit theorem is established. The results are applied to linear models with errors being short-range dependent linear processes, heavy-tailed linear processes and some widely used nonlinear time series. © Institute of Mathematical Statistics, 2007.