Hidden Markov based autoregressive analysis of stationary and non-stationary electrophysiological signals for functional coupling studies.

In this paper, we apply multivariate autoregressive (MAR) models to problems of spectral estimation for stationary and non-stationary electrophysiological data. We describe how to estimate spectral matrices and approximate confidence limits from MAR coefficients, and for stationary data spectral results obtained from the MAR approach are compared with fast Fourier transform (FFT) estimates. The hidden Markov MAR (HMMAR) model is derived for spectral estimation of non-stationary data, and traditional model order selection problems such as the number of states to include in the hidden Markov model or the choice of MAR model order are addressed through the use of a Bayesian formalism.