A Deterministic Approach to Approximation Modelling

In this paper we will describe a deterministic approach to time series analysis. The central problem consists of approximate modelling of an observed time series by means of a deterministic dynamical system. The quality of a model with respect to data will depend on the purpose of modelling. We will consider the purpose of description and that of prediction. We define the quality by means of complexity and misfit measures, expressed in terms of canonical parametrizations of dynamical systems. We give algorithms to determine optimal models for a given time series and investigate some consistency properties. Finally we present some simulations of these modelling procedures

Closed subspaces, polynomial operators in the shift, and ARMA representations

AbstractThis paper is concerned with the representation of system behaviors by equations involving polynomial shift operators. In particular, the question of the elimination of latent (i.e., auxiliary) variables from an ARMA representation is considered for the case of multidimensional systems