Testing for Unit Roots with Flow Data and Varying Sampling Frequency

This paper considers tests for a unit root in a flow variable when the span of data and/or the sampling frequency are allowed to vary. The limiting distributions of the statistics are obtained under both the null and alternative hypotheses, thereby enabling an analysis of the consistency properties of the tests to be conducted. Contrary to the situation with a stock variable, it is found that it is possible to consistently test for a unit root in a flow variable even when the span of the data is fixed, and, furthermore, that increasing the span of the data is not in itself sufficient for consistent testing. Some new simulation results are provided while the theoretical results obtained help to explain recent simulation findings by other authors involving unit root tests with flow variables.