I(2) Cointegration analysis in the presence of deterministic shifts. Working Paper, Faculty of

This paper investigates limit theory for the likelihood analysis of an I(2) coin-tegrated vector autoregressive (VAR) model in the presence of deterministic shifts. A log likelihood ratio (logLR) test statistic for integration indices is considered, and it is demonstrated that the asymptotic distribution of the statistic is given in the form of a generalised Dicky-Fuller type distribution. A logLR test statistic for restrictions on long-run and slope coe ¢ cients is also investigated, and it is proved that the statistic is asymptotically 2 distributed. Finally, an empirical analysis of macroeconomic data in Japan is performed using the I(2) VAR model subject to a deterministic shift