Can Tests for Stochastic Unit Roots Provide Useful Portmanteau Tests for Persistence?

In this paper we investigate whether or not the recently developed class of tests of the unit root null against the alternative of a stochastic unit root forms a useful statistical tool in distinguishing between time series processes whose degree of persistence is no more than that of a unit root [I(1)] process and those which display a greater degree of persistence than I(1) series, the stochastic unit root process being an example of the latter. For a wide range of processes which have been put forward as serious competitors to the I(1) process, both of a greater and lesser degree of persistence, we find, via numerical simulation methods, that broadly speaking the stochastic unit root tests do indeed appear to provide an efficacious diagnostic tool in this regard.