Exact maximum likelihood estimation of structured or unit root multivariate time series models

The exact likelihood function of a Gaussian vector autoregressive-moving average (VARMA) model is evaluated in two nonstandard cases: (a) a parsimonious structured form, such as obtained in the echelon form structure or the scalar component model (SCM) structure; (b) a partially nonstationary (integrated of order 1) model in error-correction form. The starting point is any algorithm for computing the exact likelihood of a Gaussian VARMA time series. Our algorithm also provides the parameter estimates and their standard errors. The small sample properties of our algorithm were studied by Monte Carlo methods. Examples with real data are provided.