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An Augmented Steady-State Kalman Filter to Evaluate the Likelihood of Linear and Time-Invariant State-Space Models

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Abstract

We propose a modified version of the augmented Kalman filter (AKF) to evaluate the likelihood of linear and time-invariant state-space models (SSMs). Unlike the regular AKF, this augmented steady-state Kalman filter (ASKF), as we call it, is based on a steady-state Kalman filter (SKF). We show that to apply the ASKF, it is sufficient that the SSM at hand is stationary. We find that the ASKF can significantly reduce the computational burden to evaluate the likelihood of medium- to large-scale SSMs, making it particularly useful to estimate dynamic stochastic general equilibrium (DSGE) models and dynamic factor models. Tests using a medium-scale DSGE model, namely the 2007 version of the Smets and Wouters model, show that the ASKF is up to five times faster than the regular Kalman filter (KF). Other competing algorithms, such as the Chandrasekhar recursion (CR) or a univariate treatment of multivariate observation vectors (UKF), are also outperformed by the ASKF in terms of computational efficiency.

Suggested Citation

  • Johannes Huber, 2022. "An Augmented Steady-State Kalman Filter to Evaluate the Likelihood of Linear and Time-Invariant State-Space Models," Discussion Paper Series 343, Universitaet Augsburg, Institute for Economics.
  • Handle: RePEc:aug:augsbe:0343
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    More about this item

    Keywords

    kalman filter; dsge; bayesian estimation; maximum-likelihood estimation; computational techniques;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E20 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)

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