Cointegration in macroeconomic systems: seasonality and explosive roots

This paper deals with some of the problems evolving from application of cointegration analysis to var models of economic time series. unless data have been seasonally adjusted by popular but frequently criticized routines such as census x-11 , they often exhibit seasonal patterns which are sometimes treated by including dummies in the var system. sometimes models of additional unit roots at seasonal frequencies are suggested. the latter ones lead to the conception of seasonal cointegration. there is no guarantee that the system identified by the analysis is indeed first-order integrated as implied by standard assumptions. two ways are suggested to detect unexpected explosive and non-stationary behavior: prediction and eigenvalue analysis of the state-space form. macroeconomic systems of austrian, danish, german, and u.k. data illustrate the phenomena. in one case, explosive cycles are obtained.;