The present research paper proposes an extension of the classical scalar Auto-Regressive Moving-Average (ARMA) model to real-valued Riemannian matrix manifolds. The resulting ARMA model on matrix manifolds is expressed as a non-linear discrete-time dynamical system in state-space form whose state evolves on the tangent bundle associated with the underlying manifold. A number of examples are discussed within the present contribution that aim at illustrating the numerical behavior of the proposed ARMA model. In order to measure the degree of temporal dependency between the state-values of the ARMA model, an extension of the classical autocorrelation function for scalar sequences is suggested on the basis of the geometrical features of the underlying real-valued matrix manifold.
Auto-regressive moving-average discrete-time dynamical systems and autocorrelation functions on real-valued Riemannian matrix manifolds / Fiori, Simone. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES B.. - ISSN 1531-3492. - STAMPA. - 19:9(2014), pp. 2785-2808. [10.3934/dcdsb.2014.19.2785]
Auto-regressive moving-average discrete-time dynamical systems and autocorrelation functions on real-valued Riemannian matrix manifolds
FIORI, Simone
2014-01-01
Abstract
The present research paper proposes an extension of the classical scalar Auto-Regressive Moving-Average (ARMA) model to real-valued Riemannian matrix manifolds. The resulting ARMA model on matrix manifolds is expressed as a non-linear discrete-time dynamical system in state-space form whose state evolves on the tangent bundle associated with the underlying manifold. A number of examples are discussed within the present contribution that aim at illustrating the numerical behavior of the proposed ARMA model. In order to measure the degree of temporal dependency between the state-values of the ARMA model, an extension of the classical autocorrelation function for scalar sequences is suggested on the basis of the geometrical features of the underlying real-valued matrix manifold.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.