ASYMPTOTIC INFERENCE FOR UNIT ROOT PROCESSES WITH GARCH(1,1) ERRORS
研究了带GARCH(1,1)误差的单位根过程的一步局部拟极大似然估计量，在对称分布假设下仅需二阶矩条件即可推导出单位根估计的渐近分布，并可用于构造单位根检验。
This paper investigates the so-called one-step local quasi–maximum likelihood estimator for the unit root process with GARCH(1,1) errors. When the scaled conditional errors (the ratio of the disturbance to the conditional standard deviation) follow a symmetric distribution, the asymptotic distribution of the estimated unit root is derived only under the second-order moment condition. It is shown that this distribution is a functional of a bivariate Brownian motion as in Ling and Li (1998, Annals of Statistics 26, 84–125) and can be used to construct the unit root test.The authors thank the co-editor, Bruce Hansen, and two referees for very helpful comments and suggestions. W.K. Li's research is partially supported by the Hong Kong Research Grants Council. Ling's research is supported by RGC Competitive Earmarked Research grant HKUST6113/02P.