Abstract
We establish the asymptotic theory of least absolute deviation estimators for AR(1) processes with autoregressive parameter satisfying \(n(\rho _n-1)\rightarrow \gamma\) for some fixed \(\gamma\) as \(n\rightarrow \infty\), 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 \(\gamma = 0\) or Chan and Wei (Annals of Statistics, 15, 1050–1063, 1987) and Phillips (Biometrika, 74, 535–574, 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.
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Acknowledgements
The authors would like to express their sincere gratitude to the anonymous referees and AE for helpful comments which surely lead to an improved presentation of this paper. The authors are very grateful to Huarui He, Hui Jiang, Feng Li, Yu Miao, Shaochen Wang and Qingshan Yang for the helpful discussions. Hailin Sang’s work was partially supported by the Simons Foundation Grant 586789, USA. Guangyu Yang’s work was partially supported by the Foundation of Young Scholar of the Educational Department of Henan Province Grant 2019GGJS012, China.
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Ma, N., Sang, H. & Yang, G. Least absolute deviation estimation for AR(1) processes with roots close to unity. Ann Inst Stat Math 75, 799–832 (2023). https://doi.org/10.1007/s10463-022-00864-0
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DOI: https://doi.org/10.1007/s10463-022-00864-0