Sequence-space models are becoming increasingly popular in macroeconomics, especially in the heterogeneous-agent literature. However, the econometric toolkit for users of these models remains less developed than that available for traditional state-space methods. This note introduces an algorithm for efficiently filtering unobserved shocks in linear sequence-space models. The proposed filter solves a least-squares optimization problem in closed form and returns the expectation of unobserved shocks conditional on observed data. It handles heteroskedasticity, missing observations, measurement error, and non Gaussian shock distributions. To illustrate its properties, I apply it to data simulated from a medium-scale heterogeneous-agent New Keynesian model and show that it accurately recovers the underlying structural shocks.