ABSTRACT
The UCM seen in Chapter 3 can be easily enriched to account for the effect of observable explanatory variables, or regressors. In particular, the regressors can be inserted in the equation that relates the dependent variable with the unobservable components (observation equation),
Yt = µt + ψt + γt + δ ⊤Xt + εt, (4.1)
or they can be put in the equations defining the components, for example the trend,
µt = βt−1 + µt−1 + δ ⊤Xt + ηt, (4.2)
where in both equations Xt is the vector of explanatory variables at time t and δ a vector of coefficients.
