  Despite the fact that they do not consider the temporal nature of data,
classic dimensionality reduction techniques, such as PCA, are widely applied to
time series data. In this paper, we introduce a factor decomposition specific
for time series that builds upon the Bayesian multivariate autoregressive model
and hence evades the assumption that data points are mutually independent. The
key is to find a low-rank estimation of the autoregressive matrices. As in the
probabilistic version of other factor models, this induces a latent
low-dimensional representation of the original data. We discuss some possible
generalisations and alternatives, with the most relevant being a technique for
simultaneous smoothing and dimensionality reduction. To illustrate the
potential applications, we apply the model on a synthetic data set and
different types of neuroimaging data (EEG and ECoG).
