On a simple overlapping state-space parametrization for linear time series models

We consider a new state-space parametrization for linear time series models: data driven coordinates (DDC), which provides an atlas for the manifold of (stable) p × m transfer functions of fixed McMillan degree n. Hence, DDC has similar desirable properties as more traditional overlapping parametrizations and better than classical canonical forms. Moreover, the choice of charts can be done in a data-driven manner in a very simple way. Althugh not yet as good numerically as the parametrization by data driven local coordinates (DDLC), this parametrization has the advantage of not being local. The application of DDC to maximum likelihood identification is exemplified.