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A note on low-dimensional Kalman smoothers for systems with lagged states in the measurement equation

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  • Kurz, Malte S.

Abstract

In this paper we derive a modified Kalman smoother for state space systems with lagged states in the measurement equation. This modified Kalman smoother minimizes the mean squared error (MSE). Computationally efficient algorithms that can be used to implement it in practice are discussed. We also show that the conjecture in Nimark (2015) that the output of his modified Kalman filter for this type of systems can be plugged into the standard Kalman smoother is in general not correct. The competing smoothers are compared with regards to the MSE.

Suggested Citation

  • Kurz, Malte S., 2018. "A note on low-dimensional Kalman smoothers for systems with lagged states in the measurement equation," Economics Letters, Elsevier, vol. 168(C), pages 42-45.
    • Handle: RePEc:eee:ecolet:v:168:y:2018:i:c:p:42-45
    DOI: 10.1016/j.econlet.2018.03.037
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    References listed on IDEAS

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    1. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    2. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
    3. Jacobs, Jan P.A.M. & van Norden, Simon, 2011. "Modeling data revisions: Measurement error and dynamics of "true" values," Journal of Econometrics, Elsevier, vol. 161(2), pages 101-109, April.
    4. Nimark, Kristoffer P., 2015. "A low dimensional Kalman filter for systems with lagged states in the measurement equation," Economics Letters, Elsevier, vol. 127(C), pages 10-13.
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    Cited by:

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    3. Hauber, Philipp & Schumacher, Christian & Zhang, Jiachun, 2019. "A flexible state-space model with lagged states and lagged dependent variables: Simulation smoothing," Discussion Papers 15/2019, Deutsche Bundesbank.

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    More about this item

    Keywords

    Kalman filter; Kalman smoother; Lagged states;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • 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

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