We present algorithms for computing the weights implicitly assigned to observations when estimating unobserved components, by filtering or smoothing, using a model in state space form. The algorithms are based on recursions derived from the Kalman filter and associated smoother. Since the method applies to any model with a linear state space form, it is not restricted to time-invariant systems and it can be used in a number of situations where other methods break down. Applications include the comparison of signal extraction weights with those used by nonparametric procedures and the computation of weights assigned to observations in making forecasts. © 2002 Elsevier Science B.V. All rights reserved.