Generation of time series models with given spectral properties

We give a method for generation of periodically correlated and multivariate ARIMA models whose dynamic characteristics are partially or fully specified in terms of spectral poles and zeroes or their equivalents in the form of eigenvalues/eigenvectors of associated model matrices. Our method is based on the spectral decomposition of multi-companion matrices and their factorization into products of companion matrices. Generated models are needed in simulation but may also be used in estimation, e.g. to set sensible initial values of parameters for nonlinear optimization. We are not aware of any other general method for multivariate linear systems of comparable generality and control over the spectral properties of the generated model. © 2009 Blackwell Publishing Ltd.