Spectral Rank, Feedback, Causality and the Indirect Method for CARMA Identification

2020/04/06 by Cao, Wenqi, Lindquist, Anders, Picci, Giorgio
#Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2004.02463

Abstract

Building on a recent paper by Georgiou and Lindquist [1] on the problem of rank deficiency of spectral densities and hidden dynamical relations after sampling of continuous-time stochastic processes, this paper is devoted to understanding related questions of feedback and Granger causality that affect stability properties. This then naturally connects to CARMA identification, where we remark on certain oversights in the literature.

Related

• Dynamic relations in sampled processes
• Noise recovery for L 'evy-driven CARMA processes and high-frequency\n behaviour of approximating Riemann sums
• A note on estimation of α-stable CARMA processes sampled at low frequencies
• Cause-effect inference through spectral independence in linear dynamical\n systems: theoretical foundations
• Spectral Representation of Multivariate Regularly Varying L 'evy and\n CARMA processes