Smoothness priors multichannel autoregressive time series modeling

A smoothness priors approach to the multichannel autoregressive (MVAR) modeling of stationary time series is presented. Data channels are modeled individually as in multi-input scalar-output transfer function modeling under smoothness priors constraints. The models are combined algebraically to yield a smoothness priors (SPMVAR) model. In each transfer function model, smoothness hyperparameters balance the tradeoff between the infidelity of the models to the data and the infidelity of the model to the smoothness constraints. The likelihood of the hyperparameters is maximized by a BFGS-least squares procedure. The fitted SPMVAR model yields an estimate of the power spectral density matrix of the process and the coherence, phase and transfer function. The SPMVAR method tends to be less sensitive than other MVAR methods to overparameterization and to spectral line feedthrough. Several examples are worked