Separating trend and cyclical dynamics in state space models with exogenous inputs

In the present study we compare three state rotation methods in modelling the impact of the US economy on the Finnish economy, i.e. Schur decomposition, eigenvalue analysis and singular value decomposition. Singular value decomposition is seen to provide a robust approximation of the state rotation in most cases studied, irrespective of whether the characteristic roots of the state transition matrix are complex. Thus, singular value decomposition seems to be a viable computational device not only in estimating the system matrices of the state space model, but also in state rotation, as compared to the more involved techniques based on eigenvalue analysis or Schur decomposition.