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

Dynamic factor and VARMA models: equivalent representations, dimension reduction and nonlinear matrix equations