The power problems of unit root test in time series with autoregressive errors

Monte Carlo methods are used to study the size and power of serial-correlation-corrected versions of the Dickey-Fuller (1979,1981) unit root tests appropriate when the time series has unknown mean. The modifications do not cause serious size distortions or power deterioration in the white noise case. While studies in the literature have investigated the operating characteristics of these tests in the presence of moving average errors, of particular concern in this paper is the performance of these procedures in the presence of autoregressive errors. The Philips and Perron (1988) and Choi and Philips (1991) procedures are found to suffer from serious size distortions and have very low power when errors are autoregressively correlated. We conclude that even in the most favorable cases, these tests perform poorly against trend-stationary alternatives which are plausible for annual, quarterly, and monthly macroeconomic time series. The augmented Dickey-Fuller procedure, on the other hand, is reasonably well-behaved.