Mixed normality and ancillarity in I(2) systems

This paper studies asymptotic likelihood inference on cointegration paramet ers in systems integrated of order two. We start with so-called triangular systems and then extend the analysis to vector autoregressions. We show tha t even when all unit root restrictions have been imposed, the asymptotic ob served information is not (locally) ancillary, which implies that the log-l ikelihood ratio is not locally asymptotically mixed normal. The results are applied to inference on polynomial cointegration. Some similarities and di fferences with I(1) systems are also discussed.