Dear all,

I would like to announce the following talk that will be held on Friday May 10th 2019, at 4:30 PM, in Aula D’Antoni (1101) of the Department of Mathematics, University of Rome Tor Vergata.

Speaker: Massimo Franchi (Dipartimento di Scienze Statistiche, Sapienza Università di Roma)

Title: Cointegration in Functional Autoregressive Processes

Abstract: In this talk we define the class of H-valued autoregressive (AR) processes with a unit root of finite type, where H is an infinite dimensional separable Hilbert space, and derive a generalization of the Granger-Johansen Representation Theorem valid for any integration order d = 1, 2, . . . . 

An existence theorem shows that the solution of an AR with a unit root of finite type is necessarily integrated of some finite integer d and displays a common trends representation with a finite number of common stochastic trends of the type of (cumulated) bilateral random walks and an infinite dimensional cointegrating space. A characterization theorem clarifies the connections between the structure of the AR operators and (i) the order of integration, (ii) the structure of the attractor space and the cointegrating space, (iii) the expression of the cointegrating relations, and (iv) the triangular representation of the process. 

Kind regards,

Anna Vidotto