We establish that the recursive, state-space methods of Kalman ﬁltering and smoothing can be used to implement the Doan, Litterman, and Sims (1983) approach to econometric forecast and policy evaluation. Compared with the methods outlined in Doan, Litterman, and Sims, the Kalman algorithms are more easily programmed and modiﬁed to incorporate diﬀerent linear constraints, avoid cumbersome matrix inversions, and provide estimates of the full variance-covariance matrix of the constrained projection errors which can be used directly, under standard normality assumptions, to test statistically the likelihood and internal consistency of the forecast under study.
Clarida, Richard H. and Coyle, Diane, "Conditional Projection by Means of Kalman Filtering" (1984). Cowles Foundation Discussion Papers. 935.