Title: Some results on the structure theory of cointegrated state space systems
Authors: Massimo Franchi - University of Rome La Sapienza (Italy) [presenting]
Abstract: Minimality of the state space representation of a stochastic process places restrictions on the rank of certain matrices that show up in the leading coecient of the principal part of its implied transfer functions; when unit roots are allowed for, those restrictions and the reduced rank structure of the state matrix polynomial at one shape the integration and cointegration properties of the state and the observed processes. A characterization of cointegration and polynomial cointegration in integrated state space systems is presented in the $I(d)$ case for generic integer $d$ and the leading $I(1)$ and $I(2)$ cases are discussed in detail. Extensions to multiple frequency unit roots and connections with the results in the literature are also covered.