http://repub.eur.nl/res/aut/3836/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/1543/ 1998-11-26T00:00:00Z In this paper we discuss two methods for the estimation of linear dynamic factor models. The first method is behavioural in nature and consists of the least squares approximation of the observed data by means of a linear system. The second method is based on the statistical concept of principal components and uses subspace ideas from approximate realization theory. The two methods are compared by means of simulated data. http://repub.eur.nl/res/pub/1416/ 1997-01-01T00:00:00Z The behavioural framework has several attractions to offer for the identification of multivariable systems. Some of the variables may be left unexplained without the need for a distinction between inputs and outputs; criteria for model quality are independent of the chosen parametrization; and behaviours allow for a global (i.e., non-local) approximation of the system dynamics. This is illustrated with a behavioural least squares method with an application in dynamic factor analysis. http://repub.eur.nl/res/pub/1346/ 1996-06-05T00:00:00Z This paper concerns the modelling of stochastic processes by means of dynamic factor models. In such models the observed process is decomposed into a structured part called the latent process, and a remainder that is called noise. The observed variables are treated in a symmetric way, so that no distinction between inputs and outputs is required. This motivates the condition that also the prior assumptions on the noise are symmetric in nature. One of the central questions in this paper is how uncertainty about the noise structure translates into non-uniqueness of the possible underlying latent processes. We investigate several possible noise specifications and analyse properties of the resulting class of observationally equivalent factor models. This concerns in particular the characterization of optimal models and properties of continuity and consistency. http://repub.eur.nl/res/pub/1374/ 1996-01-01T00:00:00Z Behaviours provide an elegant, parameter free characterization of deterministic systems. We discuss a possible application of behaviours in the approximation of stochastic systems. This can be seen as an extension to the dynamic case of the well-known static factor analysis model. An essential difference is that we see modelling primarily as a matter of process approximation, not as a method to recover the true data generating process. In particular we see "noise properties" as a kind of prior model assumption that can be compared with the resulting quality of the process approximation. http://repub.eur.nl/res/pub/1387/ 1996-01-01T00:00:00Z Global total least squares (GTLS) is a method for the identification of linear systems where no distinction between input and output variables is required. This method has been developed within the deterministic behavioural approach to systems. In this paper we analyse statistical properties of this method when the observations are generated by a multivariable stationary stochastic process. In particular, sufficient conditions for the consistency of GTLS are derived. This means that, when the number of observations tends to infinity, the identified deterministic system converges to the system that provides an optimal appoximation of the data generating process. The two main results are the following. GTLS is consistent if a guaranteed stability bound can be given a priori. If this information is not available, then consistency is obtained (at some loss of finite sample efficiency) if GTLS is applied to the observed data extended with zero values in past and future. http://repub.eur.nl/res/pub/1352/ 1995-01-01T00:00:00Z Global total least squares has been introduced as a method for the identification of deterministic system behaviours. We analyse this method within a stochastic framework, where the observed data are generated by a stationary stochastic process. Conditions are formulated so that the method is consistent in the sense that, when the number of observations tends to infinity, the identified deterministic behaviour converges to the behaviour that provides an optimal appoximation of the data generating process.