  Vector autoregressive (VAR) models have become a staple in the analysis of
multivariate time series and are formulated in the time domain as difference
equations, with an implied covariance structure. In many contexts, it is
desirable to work with a stable, or at least stationary, representation. To fit
such models, one must impose restrictions on the coefficient matrices to ensure
that certain determinants are nonzero; which, except in special cases, may
prove burdensome. To circumvent these difficulties, we propose a flexible
frequency domain model expressed in terms of the spectral density matrix.
Specifically, this paper treats the modeling of covariance stationary
vector-valued (i.e., multivariate) time series via an extension of the
exponential model for the spectrum of a scalar time series. We discuss the
modeling advantages of the vector exponential model and its computational
facets, such as how to obtain Wold coefficients from given cepstral
coefficients. Finally, we demonstrate the utility of our approach through
simulation as well as two illustrative data examples focusing on multi-step
ahead forecasting and estimation of squared coherence.
