IDENTIFIABILITY IN MULTIVARIATE DYNAMIC LINEAR ERRORS-IN-VARIABLES MODELS

This article considers multivariate causal transfer function systems with latent stationary inputs and outputs. Their observation is assumed to be disturbed by errors in variables (EV). The main identification results for such models so far consists of structure theory. Derived are descriptions of classes of EV transfer function systems compatible with given covariance structures of the observed variables under various causality constraints. The case of unique determination is treated only for one-dimensional models. The article derives a great variety of conditions under which a multivariate EV transfer function system is uniquely determined by the second-order moments of the observed variables. For this purpose it considers a general model class of nonparametric systems and subclasses of systems with some parameterized components having fixed order parameters. If parametric, the transfer function is a rational matrix. Parametric inputs or errors follow vector autoregressive moving average (ARMA) processes. Subclasses of systems with specific time series structures described by certain relations of the order parameters are shown to be identifiable. Consider for instance a subclass with parametric inputs xi(t) and input errors v(t) following block identifiable ARMA processes with autoregressive (AR) orders k(xi), k(upsilon) and moving average (MA) orders n(xi), n(upsilon). Transfer function and output errors are nonparametric or parametric. The subclass proves to be locally identifiable if k(xi) > n(xi) or k(upsilon) > n(upsilon), and (globally) identifiable if k(xi) > n(xi) and k(upsilon) = 0 or k(upsilon) > n(upsilon) and k(xi) = 0. Analogous conditions am given for the caw that the inputs and their errors have a more detailed AR and MA structure. By also considering subclasses of a restricted model class with diagonal covariance structure of the inputs, the results reveal the effect of contemporaneous correlation among the inputs on the state of identifiability.