By analogy with the multivariate reduced rank regression model: \(Y_ t=ABX_ t+\epsilon_ t\), where A and B are \(m\times r\) and \(r\times n\) matrices respectively, the authors investigate reduced rank models for multiple time series \[ Y_ t=A(L)B(L)Y_{t-1}+\epsilon_ t \] where L denotes the lag operator, A and B are \(m\times r\) and \(r\times n\) matrix polynomial operators of degrees \(p_ 2\) and \(p_ 1\) respectively. The estimation of parameters and associated asymptotic theory are derived. To illustrate the methods, US hog and corn data are considered.