Identification of source components in multivariate time series by state space modelling

In this paper we study the application of classical methods for dynamical modelling of time series to the task of decomposing multivariate time series into approximately independent source components, a task that has traditionally been addressed by Factor Analysis (FA) and more recently by Independent Component Analysis (ICA). Based on maximum-likelihood fitting of linear state space models we develop a new framework for this task, for which many of the limitations of standard ICA algorithms can be relieved. Through comparison of likelihood, or, more precisely, of the Akaike Information Criterion, it is demonstrated that dynamical modelling provides considerably better description of given data than FA and non-dynamical ICA. The comparison is applied to both simulated and real-world time series, the latter being given by an electrocardiogram and an electroencephalogram.