A dynamic factor model with factor series following a VAR$(p)$ model is shown to have a VARMA$(p,p)$ model representation. Reduced-rank structures are identified for the VAR and VMA components of the resulting VARMA model. It is also shown how the VMA component parameters can be computed numerically from the original model parameters via the innovations algorithm, and connections of this approach to non-linear matrix equations are made. Some VAR models related to the resulting VARMA model are also discussed.

翻译：一个因子序列服从VAR$(p)$模型的动态因子模型被证明具有VARMA$(p,p)$模型表示。在所得VARMA模型的VAR分量和VMA分量中识别出降秩结构。同时展示了如何通过新息算法，从原始模型参数数值计算VMA分量参数，并建立了该方法与非线性矩阵方程之间的联系。此外，还讨论了与所得VARMA模型相关的若干VAR模型。