USEFUL MODIFICATIONS TO SOME UNIT-ROOT TESTS WITH DEPENDENT ERRORS AND THEIR LOCAL ASYMPTOTIC PROPERTIES

Many unit root tests have distorted sizes when the root of the error p rocess is close to the unit circle. This paper analyses the properties of the Phillips-Perron tests and some of their variants in the proble matic parameter space. We use local asymptotic analyses to explain why the Phillips-Perron tests suffer from severe size distortions regardl ess of the choice of the spectral density estimator but that the modif ied statistics show dramatic improvements in size when used in conjunc tion with a particular formulation of an autoregressive spectral densi ty estimator. We explain why kernel based spectral density estimators aggravate the size problem in the Phillips-Perron tests and yield no s ize improvement to the modified statistics. The local asymptotic power of the modified statistics are also evaluated. These modified statist ics are recommended as being useful in empirical work since they are f ree of the size problems which have plagued many unit root tests, and they retain respectable power.