Modeling of Low Rank Time Series
Abstract
Rankdeficient stationary stochastic vector processes are present in many problems in network theory and dynamic factor analysis. In this paper we study hidden dynamical relations between the components of a discretetime stochastic vector process and investigate their properties with respect to stability and causality. More specifically, we construct transfer functions with a fullrank input process formed from selected components of the given vector process and having a vector process of the remaining components as output. An important question, which we answer in the negative, is whether it is always possible to find such a deterministic relation that is stable. We also show how our results could be used to investigate the structure of dynamic network models and the latent lowrank stochastic process in a dynamic factor model.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.11814
 Bibcode:
 2021arXiv210911814C
 Keywords:

 Electrical Engineering and Systems Science  Systems and Control;
 Mathematics  Dynamical Systems;
 Mathematics  Probability
 EPrint:
 In previous versions we assumed the spectral factor to be minimumphase, which is not required actually