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A bootstrap-enhanced fisher scoring algorithm for parameter estimation in state-space models

Author

Listed:
  • F. Catarina Pereira

    (University of Minho, Department of Mathematics
    University of Minho, Centre of Mathematics)

  • Marco Costa

    (University of Aveiro, Águeda School of Technology and Management)

  • A. Manuela Gonçalves

    (University of Minho, Department of Mathematics
    University of Aveiro, Centre for Research and Development in Mathematics and Applications
    University of Minho, Centre of Mathematics)

Abstract

This paper introduces a modified Fisher scoring algorithm for maximum likelihood estimation of state-space model parameters, enhanced with a bootstrap-based approximation of the Fisher information matrix. The proposed method, referred to as the Boost Fisher Scoring (BF) algorithm, aims to improve convergence and the accuracy of standard errors, particularly in small samples or under model misspecification. A robust extension (BFout) is also developed for time series containing outliers, in which bootstrap resampling is performed over cleaned standardized residuals. Extensive simulation studies compare the performance of the proposed methods with classical Fisher scoring and nonparametric bootstrap, under various scenarios of sample size, variance, and autocorrelation. The results show that the BF and BFout algorithms offer improved numerical stability and competitive accuracy, with significantly lower computational cost than full bootstrap procedures. Applications to synthetic and real temperature forecast data demonstrate the practical value of the proposed methodology for robust calibration and inference in time series modeling.

Suggested Citation

  • F. Catarina Pereira & Marco Costa & A. Manuela Gonçalves, 2026. "A bootstrap-enhanced fisher scoring algorithm for parameter estimation in state-space models," Computational Statistics, Springer, vol. 41(3), pages 1-46, April.
    • Handle: RePEc:spr:compst:v:41:y:2026:i:3:d:10.1007_s00180-026-01746-2
    DOI: 10.1007/s00180-026-01746-2
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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. Luísa Novais & Susana Faria, 2021. "Comparison of the EM, CEM and SEM algorithms in the estimation of finite mixtures of linear mixed models: a simulation study," Computational Statistics, Springer, vol. 36(4), pages 2507-2533, December.
    3. Rodríguez, Alejandro & Ruiz, Esther, 2012. "Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 62-74, January.
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