The Phillips unit root tests for polynomials of integrated processes

Abstract

We show that the Phillips (1987) unit root tests have nuisance parameter free limiting dis- tributions when applied to polynomials of integrated processes driven by linear process errors. This substantially generalizes a similar result of Wagner (2012) allowing only for serially uncor- related errors. The result is based on novel kernel weighted sum limit results involving powers of integrated processes. These results allow us also consider additional modifications of the Phillips (1987) tests applicable to polynomials of integrated processes.