Asymptotic Properties of the M-estimation for an AR(1) Process with a General Autoregressive Coefficient

Xinghui Wang (), Wenjing Geng (), Ruidong Han () and Qifa Xu ()
Additional contact information
Xinghui Wang: Anhui University
Wenjing Geng: Anhui University
Ruidong Han: Renmin University of China
Qifa Xu: Hefei University of Technology

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 1, 1-23

Abstract: Abstract In this paper, we consider a first-order autoregressive process with a general autoregressive coefficient. Asymptotic behaviors of an M-estimator of the autoregressive coefficient are established for the nearly stationary and mildly explosive cases, respectively. The rate of convergence of the robust estimators for the two cases are provided. The results extend ones for the least squares and least absolute deviation estimators to the robust estimator under the weaker initial conditions in the literature. Some simulations are carried out to assess the performance of our procedure.

Keywords: Limit distribution; Moderate deviations; M-estimate; Unit root; 60G10; 62M10; 62F12 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-023-10005-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-10005-6

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-023-10005-6

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().