Separation in Cointegrated Systems, Long Memory Components and Common Stochastic Trends

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 parsimonous representation of the time 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 decompositions and long- and short-memory factorisations of a multivariate time series will be affected when considering different types of separation. Generalisations to non-linear error correction models are also discussed