Separation in Cointegrated Systems and Persistent-Transitory Decompositions

The notion of separation in cointegrated systems helps identifying possible sub-system structures that may reduce the complexity of larger systems by yielding a more parsimonious representation of the times series. In this paper we demonstrate that although the subsystem cointegration analysis in such systems can be conducted in case of both completely and partially separated systems, the dual approach, i.e. calculation of the common stochastic trends, may turn out to yield properties of the trends that differ depending upon the type of separation under consideration. In particular, we demonstrate how persistent-transitory (P-T) decompositions and long- and short-memory factorizations of a multivariate time series will interact across systems when considering the presence (or absence) of different types of separation. Generalizations to non-linear error correction models are briefly discussed.