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

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Listed:
  • Ruidong Han

    (Anhui University)

  • Xinghui Wang

    (Anhui University)

  • Shuhe Hu

    (Anhui University)

Abstract

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.

Suggested Citation

  • Ruidong Han & Xinghui Wang & Shuhe Hu, 2018. "Asymptotics of the weighted least squares estimation for AR(1) processes with applications to confidence intervals," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 479-490, August.
    • Handle: RePEc:spr:stmapp:v:27:y:2018:i:3:d:10.1007_s10260-017-0406-y
    DOI: 10.1007/s10260-017-0406-y
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    References listed on IDEAS

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