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

Nannan Ma (), Hailin Sang () and Guangyu Yang ()
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Nannan Ma: Agricultural Bank of China
Hailin Sang: University of Mississippi
Guangyu Yang: Zhengzhou University

Annals of the Institute of Statistical Mathematics, 2023, vol. 75, issue 5, No 4, 799-832

Abstract: Abstract We establish the asymptotic theory of least absolute deviation estimators for AR(1) processes with autoregressive parameter satisfying $$n(\rho _n-1)\rightarrow \gamma$$ n ( ρ n - 1 ) → γ for some fixed $$\gamma$$ γ as $$n\rightarrow \infty$$ 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 $$\gamma = 0$$ γ = 0 or Chan and Wei (Annals of Statistics, 15, 1050–1063, 1987) and Phillips (Biometrika, 74, 535–574, 1987) in the case $$\gamma \ne 0$$ γ ≠ 0 . Simulation experiments are conducted to confirm the theoretical results and to demonstrate the robustness of the least absolute deviation estimation.

Keywords: Asymptotic distribution; Autoregressive processes; Least absolute deviation estimation; Local to unity; Unit root test (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10463-022-00864-0

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