A note on low-dimensional Kalman smoothers for systems with lagged states in the measurement equation

In this paper we derive a modified Kalman smoother for state space systems with lagged states in the measurement equation. This modified Kalman smoother minimizes the mean squared error (MSE). Computationally efficient algorithms that can be used to implement it in practice are discussed. We also show that the conjecture in Nimark (2015) that the output of his modified Kalman filter for this type of systems can be plugged into the standard Kalman smoother is in general not correct. The competing smoothers are compared with regards to the MSE.