Pitfall of unit autoregressive root testing

This paper examines whether the usually tested unit autoregressive (AR) root null hypothesis can be informative about the presence of a unit AR root (integration). This is considered null in generic models when the underlying time series is mean or linear trend stationary. It is concluded that non rejection of the unit AR root null hypothesis is not sufficient for integration of a time series. For sufficiency, absence of a unit MA root from the MA representation of the first difference is required. Hence, the analysis here is in line with the general statistical argument that non rejection of a null should not be taken as acceptance of the null; a false practice which is widespread in the unit root and (especially) cointegration literature. An empirical example, involving real quarterly UK GDP, is also provided.