  We show Vector Autoregressive Moving Average models with scalar Moving
Average components could be estimated by generalized least square (GLS) for
each fixed moving average polynomial. The conditional variance of the GLS model
is the concentrated covariant matrix of the moving average process. Under GLS
the likelihood function of these models has similar format to their VAR
counterparts. Maximum likelihood estimate can be done by optimizing with
gradient over the moving average parameters. These models are inexpensive
generalizations of Vector Autoregressive models. We discuss a relationship
between this result and the Borodin-Okounkov formula in operator theory.
