Testing for a Unit Root by Generalized Least Squares Methods in the Time and Frequency Domains

New time and frequency domain tests for the presence of a unit root are developed. The tests are based on generalized least squares (GLS) methods in both the time and the frequency domains. For the time domain tests, moving average processes are assumed for the error terms on the autoregression. For the frequency domain tests, general assumptions are made which allow for stationary and weakly dependent error processes. The limiting distributions of feasible GLS tests are derived under MA(1) errors in the time domain. This theory is extended to higher order moving average processes under an invertibility condition. The limiting distributions of both full and band spectrum tests in the frequency domain are also derived.

All of these limiting distributions are shown to be free of nuisance parameters. Some results on test consistency are also reported. Extensive Monte Carlo simulations are performed to study the size and power of the proposed tests in finite samples.