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

Ruidong Han, Xinghui Wang () and Shuhe Hu
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Ruidong Han: Anhui University
Xinghui Wang: Anhui University
Shuhe Hu: Anhui University

Statistical Methods & Applications, 2018, vol. 27, issue 3, No 6, 479-490

Abstract: 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.

Keywords: Weighted least squares estimation; Empirical likelihood; Interval estimation; Autoregressive models; 62F12; 60G10; 62G20 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10260-017-0406-y

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