Testing for a Unit Root with Near-Integrated Volatility

This paper considers tests for a unit root when the innovations follow a near-integrated GARCH process. We compare the asymptotic properties of the likelihood ratio statistic with that of the leastsquares based Dickey-Fuller statistic. We first use asymptotics where the GARCH variance process is stationary with fixed parameters, and then consider parameter sequences such that the GARCH process converges to a diffusion process. In both cases, we find a substantial asymptotic local power gain of the likelihood ratio test for parameter values that imply heavy tails in the unconditional innovation distribution. An empirical application to the term structure of interest rates in the Netherlands illustrates the proposed procedures.