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A data-cleaning augmented Kalman filter for robust estimation of state space models

Author

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  • Marczak, Martyna
  • Proietti, Tommaso
  • Grassi, Stefano

Abstract

A robust augmented Kalman filter (AKF) is presented for the general state space model featuring non-stationary and regression effects. The robust filter shrinks the observations towards their one-step-ahead prediction based on the past, by bounding the effect of the information carried by a new observation according to an influence function. When maximum likelihood estimation is carried out on the replacement data, an M-type estimator is obtained. The performance of the robust AKF is investigated in two applications using as a modeling framework the basic structural time series model—a popular unobserved components model in the analysis of seasonal time series. First, a Monte Carlo experiment is conducted in order to evaluate the comparative accuracy of the proposed method for estimating the variance parameters. Second, the method is applied in a forecasting context to a large set of European trade statistics series.

Suggested Citation

  • Marczak, Martyna & Proietti, Tommaso & Grassi, Stefano, 2018. "A data-cleaning augmented Kalman filter for robust estimation of state space models," Econometrics and Statistics, Elsevier, vol. 5(C), pages 107-123.
  • Handle: RePEc:eee:ecosta:v:5:y:2018:i:c:p:107-123
    DOI: 10.1016/j.ecosta.2017.02.002
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    References listed on IDEAS

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    1. Marczak, Martyna & Proietti, Tommaso, 2016. "Outlier detection in structural time series models: The indicator saturation approach," International Journal of Forecasting, Elsevier, vol. 32(1), pages 180-202.
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    More about this item

    Keywords

    Robust filtering; Augmented Kalman filter; Structural time series model; Additive outlier; Innovation outlier;

    JEL classification:

    • 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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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