Testing for a unit root under errors with just barely infinite variance
This article investigates the problem of testing for a unit root in the case that the error, {u_t}, of the model is a strictly stationary, mixing process with just barely infinite variance. Such errors have the property that for every &dgr; such that 0 <= &dgr; < 2, the moments E|u_t|-super-&dgr; are finite. Under some additional restrictions on the rate of decay of the mixing rates, these errors belong to the domain of the non-normal attraction of the normal law and obey the invariance principle. This in turn implies that there might be conditions under which the usual Phillips-type test statistics for unit roots may still converge to the corresponding Dickey-Fuller distributions. In such a case, the unit-root hypothesis can be tested within an infinite-variance framework without any modifications to either the tests themselves or the critical values employed. This article derives a necessary and sufficient condition for convergence of the standard test statistics to the Dickey-Fuller distributions. By means of Monte Carlo simulations, the article also shows that this condition is likely to hold in the case that {u_t} is a serially correlated, integrated generalized autoregressive conditionally heteroskedastic (IGARCH) process and the standard unit-root tests work well. Copyright 2008 The Authors. Journal compilation 2008 Blackwell Publishing Ltd
