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

作者：Han, Ruidong; Wang, Xinghui^*; Hu, Shuhe

来源：Statistical Methods and Applications, 2018, 27(3): 479-490.

DOI：10.1007/s10260-017-0406-y

• Weighted least squares estimation
• Empirical likelihood
• Interval estimation
• Autoregressive models

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.

• 出版日期2018-8
• 单位安徽大学