报告时间：7月1日下午1：00-2:00
报告地点：统计楼103
Title: Unit Root Test and Weighted Least Squares Estimator for an AR Process with Possible GARCH Errors
Speaker: Liang Peng, Georgia State University, Professor
Abstract: Chan and Zhang (2010) studied a unit root test based on the least squares estimator for an AR(1) model with GARCH(1,1) errors, where the asymptotic limit depends on the moments of the errors and is nonnormal if the error has an infinite variance. Zhang and Ling (2015) showed that the least squares estimator for a stationary AR model with G-GARCH errors is inconsistent if the error has an infinite variance. Therefore, it is useful to provide a unified unit root test without requiring any prior on the moments of the errors and a consistent estimator for the stationary case. Motivated by the unified empirical likelihood inference in Chan, Li and Peng (2012), this paper proposes a unified empirical likelihood test for testing unit root in an AR(1) model with GARCH(p,q) errors, whose limit is always a chi-squared distribution with one degree of freedom. Furthermore, an empirical likelihood inference is provided for a stationary AR process with GARCH(p,q) errors, which results in consistent estimation regardless of the heaviness of the tails. The proposed estimator is different from the self-weighted least absolute deviations estimator in Zhu and Ling (2015), where the innovation in the GARCH errors is assumed to have median zero instead of mean zero. A simulation study confirms the good finite sample performance of the proposed methods before we apply them to some real data sets in finance.