Precision-based sampling for state space models that have no measurement error - Elmar Mertens (Deutsche Bundesbank, 2023)
This article presents a computationally efficient approach to sample from Gaussian state space models. The method is an instance of precision-based sampling methods that operate on the inverse variance-covariance matrix of the states (also known as precision). The novelty is to handle cases where the observables are modeled as a linear combination of the states without measurement error. In this case, the posterior variance of the states is singular and precision is ill-defined. As in other instances of precision-based sampling, computational gains are considerable. Relevant applications include trend-cycle decompositions, (mixed-frequency) VARs with missing variables and DSGE models.
Keywords: C11; C32; C51; 330; State space models; signal extraction; Kalman filter and smoother; precision-based sampling; band matrix