For the general state-space model in Eqs. (11.26) and (11.27), we consider two cases of missing values. First, suppose that similar to the local trend model in Section 11.1 the observations yt at t = ℓ + 1, … , ℓ + h are missing. In this case, there is no new information available at these time points and we set
The Kalman filter in Eq. (11.64) can then proceed as usual. That is,
for t = ℓ + 1, … , ℓ + h. Similarly, the smoothed state vectors can be computed as usual via Eq. (11.74) with
for t = ℓ + 1, … , ℓ + h.
In the second case, some components of yt are missing. Let 
be the vector of observed data at time t, where J is an indicator matrix identifying the observed data. More specifically, rows of J are a subset of the rows of the k × k identity matrix. In this case, the observation equation (11.27) of the model can be transformed as
where 
, 
, and 
= Jet with covariance matrix Var(
. The Kalman filter and state-smoothing recursion continue to apply except that the modified observation equation is used at time t. Consequently, the ease in handling missing values is a nice feature of the state-space model.