ABSTRACT
This chapter describes the two basic state-space (SS) formulations: a multiple error model (MEM) because it allows for different errors in the state and observation equations of the model, and the single error model (SEM) having a unique vector of random disturbances. The relationship between both MEM and SEM formulations is very rich, and can be summarized in two ideas. First, under nonrestrictive assumptions a MEM model can be written in an observationally equivalent SEM form. Second, the SEM has specific advantages for applications requiring precise estimates of the state variables. The combination of both ideas allows one to devise powerful computational procedures. The chapter presents the main properties of the SS model using the MEM representation, bearing in mind that their extension to the SEM case is trivial. It also shows how to write a standard linear stochastic process in SEM form.
