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Maximum Likelihood Estimation of Regression Effects in State Space Models

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  • Qian Hang

    (The MathWorks, Inc., 55 Centre Street, Natick, MA 01760, USA)

Abstract

Unknown parameters, including regression coefficients, in state space models can be estimated by maximum likelihood. An alternative approach is to augment the state vector to include regression coefficients. However, the state estimator obtained by the Kalman filter is numerically different from the maximum likelihood estimator. We address the discrepancy by a novel method based on proper distributions returned by the ordinary Kalman filter without dependency on diffuse initialization. We prove that maximizing a low-dimensional objective function that combines the likelihood, the filtering mean and variance can reproduce the high-dimensional maximum likelihood results.

Suggested Citation

  • Qian Hang, 2025. "Maximum Likelihood Estimation of Regression Effects in State Space Models," Journal of Econometric Methods, De Gruyter, vol. 14(1), pages 13-19.
    • Handle: RePEc:bpj:jecome:v:14:y:2025:i:1:p:13-19:n:1001
    DOI: 10.1515/jem-2024-0020
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