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Asymptotic inference of least absolute deviation estimation for AR(1) processes

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  • Xinghui Wang
  • Huilong Wang
  • Hongrui Wang
  • Shuhe Hu

Abstract

In this article, we consider a first-order autoregressive process yt=ρnyt−1+ut with n|1−ρn|→∞ as n→∞. The Gaussian limit theory and the Cauchy limit theory of the least absolute deviation estimator for the near-stationary process (ρn∈[0,1)) and the mildly explosive process (ρn>1) are derived, respectively. The results are complementary to the uniform limit theory of least squares estimators for stationary autoregressions in Giraitis and Phillips (2006). Some simulations are carried out to assess the performance of our procedure.

Suggested Citation

  • Xinghui Wang & Huilong Wang & Hongrui Wang & Shuhe Hu, 2020. "Asymptotic inference of least absolute deviation estimation for AR(1) processes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(4), pages 809-826, February.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:4:p:809-826
    DOI: 10.1080/03610926.2018.1549252
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    Cited by:

    1. 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.

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