A characterization of vector autoregressive processes with common cyclical features

This paper presents necessary and sufficient conditions for the existence of common cyclical features in
Vector Auto Regressive (VAR) processes integrated of order 0, 1, 2, where the common cyclical features
correspond to common serial correlation (CS), commonality in the final equations (CE) and co-dependence
(CD). The results are based on local rank factorizations of the reversed AR polynomial around the poles
of its inverse. All processes with CS structures are found to present also CE structures and vice versa. The
presence of CD structures, instead, implies the presence of both CS and CE structures, but not vice versa.
Characterizations of the CS, CE, CD linear combinations are given in terms of linear subspaces defined in
the local rank factorizations.