The article discusses how to estimate and check vector ARMA time series models using maximum likelihood methods. It explains how to find the best estimates for the model's parameters and how to test if certain constraints apply to these parameters. The researchers also explore ways to check if the estimated model fits the data well by looking at the correlation of the model's errors. Additionally, they consider how errors in parameter estimation can affect the accuracy of predictions made by the model. Overall, the article provides practical guidance on fitting and evaluating vector ARMA models.