Estimation for nearly unit root processes with GARCH errors

Abstract

In this paper the limiting distribution of the least square estimate for the autoregressive coefficient of a nearly unit root model with GARCH errors is derived. Since the limiting distribution depends on the unknown variance of the errors, an empirical likelihood ratio statistic is proposed from which confidence intervals can be constructed for the nearly unit root model without knowing the variance. To gain an intuitive sense for the empirical likelihood ratio, a small simulation for the asymptotic distribution is given.