The problem of parametric autoregressive model-based estimation of a time-varying spectral density function of a multivariate nonstationary process is considered. It is shown that estimation results can be considerably improved if identification of the autoregressive model is carried out using the two-sided doubly exponentially weighted lattice algorithm, which combines results yielded by two one-sided lattice algorithms running forward in time and backward in time, respectively. It is also shown that the model order and the most appropriate estimation bandwidth can be efficiently selected using the suitably modified Akaikes final prediction error criterion.