The structure of multivariate AR and ARMA systems: Regular and singular systems; the single and the mixed frequency case

Abstract

This paper is concerned with the structure of multivariate AR and ARMA systems. The emphasis is on two “non-standard” cases: We deal with the structure of singular AR and ARMA systems which generate singular spectral densities and with identifiability of ARMA systems from mixed frequency data. In the mixed frequency case we show that, for the case where the MA order is smaller than or equal to the AR order, identifiability can be achieved generically. Furthermore, we demonstrate that for a pure MA system identifiability cannot be achieved. The paper generalizes the results obtained in Anderson et al. (2015) for the AR case.