One channel at-a-time multichannel autoregressive modeling: applications to stationary and nonstationary covariance time series

Abstract

The research explores and develops a new strategy for the multichannel (multivariate) autoregressive (MCAR) time series modeling of multichannel stationary and nonstationary time series. The multichannel time series modeling is achieved doing things one channel at-a-time using only scalar computations on instantaneous data. Under the one channel at-a-time modeling paradigm, three long standing and important problems in multichannel time series modeling are studied. First, one channel at-a-time scalar autoregressive (AR) time series modeling in combination with subset selection and a subsequent linear transformation achieves a relatively parsimonious multichannel autoregressive model of stationary time series and reduced one-step-ahead prediction variance as compared to conventional MCAR model fitting. Second, enhanced power spectral density estimation for multichannel stationary time series may be achieved with one channel at-a-time multichannel AR modeling in combination with a smoothness priors distribution on the scalar AR model parameters. Third, estimates of the time varying power spectral density matrix for multichannel nonstationary covariance time series are achieved using the one channel at-a-time paradigm in conjunction with a Bayesian smoothness priors stochastic linear regression model of the partial correlation coefficients (PARCORS) of a scalar lattice AR model. In this case, only a small number of hyper-parameters are fitted for the multichannel time varying AR model which has many more parameters than data.