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Precision-based sampling for state space models that have no measurement error

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  • Mertens, Elmar

Abstract

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.

Suggested Citation

  • Mertens, Elmar, 2023. "Precision-based sampling for state space models that have no measurement error," Discussion Papers 25/2023, Deutsche Bundesbank.
  • Handle: RePEc:zbw:bubdps:252023
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    More about this item

    Keywords

    State space models; signal extraction; Kalman filter and smoother; precision-based sampling; band matrix;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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