State Space Estimation: from Kalman Filter Back to Least Squares

This note reviews a direct least squares estimation of a state space model and highlights its advantages over the standard Kalman filter in some applications. Although there is a close relationship between these two concepts, dual understanding of the estimation problem seems to be little appreciated by the mainstream econometric literature as well as applied researchers. Due to computational and theoretical advancements, the least squares estimation of a state space model has become a viable alternative in many fields, showing great potential in solving otherwise difficult problems. This note gathers and discusses some possible applications to illustrate the point and contribute to their wider use in practice.