16.6 State-space form of ARMA(p,q) models

There is a large class of models in the statistical finance literature that have the form \[\begin{equation*} \begin{gathered} \mathbf{x}_{t+1} = \mathbf{B}\mathbf{x}_t + \boldsymbol{\Gamma}\boldsymbol{\eta}_t\\ \mathbf{y}_t = \mathbf{Z}\mathbf{x}_t + \boldsymbol{\eta}_t\\ \end{gathered} \end{equation*}\] For example, ARMA(p,q) models can be written in this form. The MARSS model framework in this package will not allow you to write models in that form. You can put the \(\boldsymbol{\eta}_t\) into the \(\mathbf{x}_t\) vector and set \(\mathbf{R}=0\) to make models of this form using the MARSS form, but the EM algorithm in the MARSS package won’t let you estimate parameters because the parameters will drop out of the full likelihood being maximized in the algorithm. You can try using BFGS by passing in the method="BFGS" to the MARSS() call.