ABSTRACT
This chapter discusses a numerical procedure to do the inverse transformation, that is, to obtain the coefficients of the VARMAX representation for any linear state-space (SS) model. The fact that there are procedures to go from VARMAX to SS form and vice versa has a clear and interesting consequence: both representations are equally general and choosing between them is just a matter of convenience. Beyond this theoretical implication, these procedures are also useful to solve three practical problems: discussing the identifiability of an SS model, performing diagnostic checks, and calibrating the SS model parameters to ensure that it realizes any given reduced-form VARMAX. The chapter discusses these applications and provides practical examples.
