Let $\left\{{W}_{t}\right\}=\left\{{({X}_{{t}^{\text{'}}}^{\text{'}},{Y}_{t}^{\text{'}})}^{\text{'}}\right\}$ be vector ARMA $(m,n)$ processes. Denote by ${\widehat{X}}_{t}\left(a\right)$ the predictor of ${X}_{t}$ based on ${X}_{t-a},{X}_{t-a-1},...$ and by ${\widehat{X}}_{t}(a,b)$ the predictor of ${X}_{t}$ based on ${X}_{t-a},{X}_{t-a-1},...,{Y}_{t-b},{Y}_{t-b-1},...$. The accuracy of the predictors is measured by ${\Delta}_{X}\left(a\right)=\text{E}[{X}_{t}-{\widehat{X}}_{t}\left(a\right)]{[{X}_{t}-{\widehat{X}}_{t}\left(a\right)]}^{\text{'}}$ and ${\Delta}_{X}(a,b)=\text{E}[{X}_{t}-{\widehat{X}}_{t}(a,b)]{[{X}_{t}-{\widehat{X}}_{t}(a,b)]}^{\text{'}}$. A general sufficient condition for the equality ${\Delta}_{X}\left(a\right)={\Delta}_{X}(a,a)]$ is given in the paper and it is shown that the equality ${\Delta}_{X}\left(1\right)={\Delta}_{X}(1,1)]$ implies ${\Delta}_{X}\left(a\right)={\Delta}_{X}(a,a)]$ for all natural numbers $a$.