Asymptotic Inference for Unit Root Processes with GARCH(1,1) Errors

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