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

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  • Nannan Ma

    (Agricultural Bank of China)

  • Hailin Sang

    (University of Mississippi)

  • Guangyu Yang

    (Zhengzhou University)

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.

Suggested Citation

  • Nannan Ma & Hailin Sang & Guangyu Yang, 2023. "Least absolute deviation estimation for AR(1) processes with roots close to unity," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(5), pages 799-832, October.
    • Handle: RePEc:spr:aistmt:v:75:y:2023:i:5:d:10.1007_s10463-022-00864-0
    DOI: 10.1007/s10463-022-00864-0
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