Unit Roots in Economic and Financial Time Series: A Re-Evaluation based on Enlightened Judgement

This paper re-evaluates the key past results of unit root test, emphasizing that the use of a conventional level of significance is not in general optimal due to the test having low power. The optimal levels for popular unit root tests, chosen using the line of enlightened judgement under a symmetric loss function, are found to be much higher than conventional ones. We also propose simple calibration rules for the optimal level of significance for a range of unit root tests based on asymptotic local power. At the optimal levels, many time series in the extended Nelson-Plosser data set are judged to be trend-stationary, including real income variables, employment variables and money stock. We also find nearly all real exchange rates covered in the Elliott-Pesavento study to be stationary at the optimal levels, which lends strong support for the purchasing power parity. Additionally, most of the real interest rates covered in the Rapach-Weber study are found to be stationary.