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

01/05/2023

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by   Nannan Ma, et al.

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