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We show Vector Autoregressive Moving Average models with scalar MovingAverage components could be estimated by generalized least square (GLS) foreach fixed moving average polynomial. The conditional variance of the GLS modelis the concentrated covariant matrix of the moving average process. Under GLSthe likelihood function of these models has similar format to their VARcounterparts. Maximum likelihood estimate can be done by optimizing withgradient over the moving average parameters. These models are inexpensivegeneralizations of Vector Autoregressive models. We discuss a relationshipbetween this result and the Borodin-Okounkov formula in operator theory.

Vector Autoregressive Moving Average Model with Scalar Moving Average