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Ma, Nannan; Sang, Hailin; Yang, Guangyu
Annals of the Institute of Statistical Mathematics, 10/2023, Letnik: 75, Številka: 5Journal Article
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 (Journal of Time Series Analysis, 29, 203–212, 2008) in the case γ = 0 or Chan and Wei (Annals of Statistics, 15, 1050–1063, 1987) and Phillips (Biometrika, 74, 535–574, 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.
