A Randomized Procedure for Choosing Data Transformation

Standard unit root and stationarity tests (see e.g. Dickey and Fuller (1979)) assume linearity under both the null and the alternative hypothesis. Violation of this linearity assumption can result in severe size and power distortion, both in finite and large samples. Thus, it is reasonable to address the problem of data transformation before running a unit root test. In this paper we propose a simple randomized procedure, coupled with sample conditioning, for choosing between levels and log-levels specifications in the presence of deterministic and/or stochastic trends. In particular, we add a randomized component to a basic test statistic, proceed by conditioning on the sample, and show that for all samples except a set of measure zero, the statistic has a X2 limiting distribution under the null hypothesis (log linearity), while it diverges under the alternative hypothesis (level linearity). Once we have chosen the proper data transformation, we remain with the standard problem of testing for a unit root, either in levels or in logs. Monte Carlo findings suggest that the proposed test has good finite sample properties for samples of at least 300 observations. In addition, an examination of the King, Plosser, Stock and Watson (1991) data set is carried out, and evidence in favor of using logged data is provided.