Testing for unit root processes in random coefficient autoregressive models

This paper proposes new tests for simple unit root and unit root with a possibly nonzero drift processes, in the context of a random coefficient autoregressive model. The asymptotic distributions of the tests are derived, and their properties are investigated through a Monte Carlo experiment. The tests have good power properties, and in many cases they perform better than the competing univariate tests available in the literature, despite testing for a multiple joint hypothesis. In particular, for moderate to large sample sizes, very small values of the variance of the random coefficient variable are needed in order for the tests to reach some power against roots very close to unity. Finally, the proposed tests are applied to the US GDP series.