Least absolute deviation estimation for AR(1) processes with roots close to unity

TL;DR

This paper develops the asymptotic theory for least absolute deviation estimators in AR(1) processes with roots near unity, extending existing results for OLS estimators and confirming robustness through simulations.

Contribution

It provides the first asymptotic analysis of LAD estimators for near-unit root AR(1) models, generalizing prior OLS results to a robust estimation context.

Findings

Asymptotic distribution derived for LAD estimators near unit roots

Simulation confirms theoretical predictions and robustness of LAD estimators

Extension of existing AR(1) estimation theory to LAD methods

Abstract

We establish the asymptotic theory of least absolute deviation estimators for AR(1) processes with autoregressive parameter satisfying $n(\rho_n-1)\to\gamma$ for some fixed $\gamma$ as $n\to\infty$, which is parallel to the results of ordinary least squares estimators developed by Andrews and Guggenberger (2008) in the case $\gamma=0$ or Chan and Wei (1987) and Phillips (1987) in the case $\gamma\ne 0$. Simulation experiments are conducted to confirm the theoretical results and to demonstrate the robustness of the least absolute deviation estimation.