Statistical Methods & Applications

, Volume 27, Issue 3, pp 479–490 | Cite as

Asymptotics of the weighted least squares estimation for AR(1) processes with applications to confidence intervals

  • Ruidong Han
  • Xinghui WangEmail author
  • Shuhe Hu
Original Paper


For the first-order autoregressive model, we establish the asymptotic theory of the weighted least squares estimations whether the underlying autoregressive process is stationary, unit root, near integrated or even explosive under a weaker moment condition of innovations. The asymptotic limit of this estimator is always normal. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. An empirical likelihood confidence interval is proposed for interval estimations of the autoregressive coefficient. The results improve the corresponding ones of Chan et al. (Econ Theory 28:705–717, 2012). Some simulations are conducted to illustrate the proposed method.


Weighted least squares estimation Empirical likelihood Interval estimation Autoregressive models 

Mathematics Subject Classification

62F12 60G10 62G20 



The authors thank the Editor-in-Chief Tommaso Proietti and two anonymous referees for their helpful comments and valuable suggestions that greatly improved the paper. This work is supported by the National Natural Science Foundation of China (11701005, 11671012, 11501004, 11501005), the Natural Science Foundation of Anhui Province (1608085QA02), the Science Fund for Distinguished Young Scholars of Anhui Province (1508085J06) and Introduction Projects of Anhui University Academic and Technology Leaders.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of EconomicsAnhui UniversityHefeiPeople’s Republic of China
  2. 2.School of Mathematical ScienceAnhui UniversityHefeiPeople’s Republic of China

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