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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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    1. Lixing Zhu & Liugen Xue, 2006. "Empirical likelihood confidence regions in a partially linear single‐index model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 549-570, June.
    2. Shi, Jian & Lau, Tai-Shing, 2000. "Empirical Likelihood for Partially Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 132-148, January.
    3. Qihua Wang & J. N. K. Rao, 2002. "Empirical Likelihood‐based Inference in Linear Models with Missing Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 563-576, September.
    4. Shiqing Ling, 2005. "Self‐weighted least absolute deviation estimation for infinite variance autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 381-393, June.
    5. Li, Jinyu & Liang, Wei & He, Shuyuan, 2011. "Empirical likelihood for LAD estimators in infinite variance ARMA models," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 212-219, February.
    6. Han, Chirok & Phillips, Peter C. B. & Sul, Donggyu, 2011. "Uniform Asymptotic Normality In Stationary And Unit Root Autoregression," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1117-1151, December.
    7. Ngai Hang Chan & Liang Peng, 2005. "Weighted least absolute deviations estimation for an AR(1) process with ARCH(1) errors," Biometrika, Biometrika Trust, vol. 92(2), pages 477-484, June.
    8. So, Beong Soo & Shin, Dong Wan, 1999. "Cauchy Estimators For Autoregressive Processes With Applications To Unit Root Tests And Confidence Intervals," Econometric Theory, Cambridge University Press, vol. 15(2), pages 165-176, April.
    9. Qihua Wang, 2002. "Empirical likelihood-based inference in linear errors-in-covariables models with validation data," Biometrika, Biometrika Trust, vol. 89(2), pages 345-358, June.
    10. Chen, Xia & Cui, Hengjian, 2008. "Empirical likelihood inference for partial linear models under martingale difference sequence," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2895-2901, December.
    11. Wang, Qi-Hua & Jing, Bing-Yi, 1999. "Empirical likelihood for partial linear models with fixed designs," Statistics & Probability Letters, Elsevier, vol. 41(4), pages 425-433, February.
    12. Anna Mikusheva, 2007. "Uniform Inference in Autoregressive Models," Econometrica, Econometric Society, vol. 75(5), pages 1411-1452, September.
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