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Filtering And Smoothing In State Space Models With Partially Diffuse Initial Conditions

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  • Craig F. Ansley
  • Robert Kohn

Abstract

. Ansley and Kohn (Annals of Statistics, 1985) generalized the Kalman filter to handle state space models with partially diffuse initial conditions and used this filter to compute the marginal likelihood of the observations efficiently. In this paper we simplify the algorithm and make it numerically more accurate and operationally more efficient. Based on this filtering algorithm we obtain a corresponding smoothing algorithm for the state vector.

Suggested Citation

  • Craig F. Ansley & Robert Kohn, 1990. "Filtering And Smoothing In State Space Models With Partially Diffuse Initial Conditions," Journal of Time Series Analysis, Wiley Blackwell, vol. 11(4), pages 275-293, July.
    • Handle: RePEc:bla:jtsera:v:11:y:1990:i:4:p:275-293
    DOI: 10.1111/j.1467-9892.1990.tb00058.x
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    Cited by:

    1. Adrian Pizzinga & Marcelo Fernandes, 2021. "Extensions to the invariance property of maximum likelihood estimation for affine‐transformed state‐space models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(3), pages 355-371, May.
    2. Koopman, Siem Jan & Harvey, Andrew, 2003. "Computing observation weights for signal extraction and filtering," Journal of Economic Dynamics and Control, Elsevier, vol. 27(7), pages 1317-1333, May.
    3. Pollock, D. S. G., 2003. "Recursive estimation in econometrics," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 37-75, October.
    4. Marc K. Francke & Siem Jan Koopman & Aart F. De Vos, 2010. "Likelihood functions for state space models with diffuse initial conditions," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(6), pages 407-414, November.
    5. José Casals & Sonia Sotoca & Miguel Jerez, 2012. "Minimally Conditioned Likelihood for a Nonstationary State Space Model," Documentos de Trabajo del ICAE 2012-04, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    6. Moro, Daniele & Sckokai, Paolo & Mazzocchi, Mario, 2000. "A New Strategy For Testing Convergence In Tastes," 2000 Annual meeting, July 30-August 2, Tampa, FL 21759, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    7. Proietti, Tommaso, 2007. "Signal extraction and filtering by linear semiparametric methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 935-958, October.
    8. Stephen Pollock, 2002. "Recursive Estimation in Econometrics," Working Papers 462, Queen Mary University of London, School of Economics and Finance.
    9. Shively, Thomas S. & Kohn, Robert, 1997. "A Bayesian approach to model selection in stochastic coefficient regression models and structural time series models," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 39-52.
    10. Webel, Karsten, 2022. "A review of some recent developments in the modelling and seasonal adjustment of infra-monthly time series," Discussion Papers 31/2022, Deutsche Bundesbank.
    11. John Tsimikas & Johannes Ledolter, 1998. "Analysis of Multi-Unit Variance Components Models with State Space Profiles," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(1), pages 147-164, March.
    12. Wong, Chi-ming & Kohn, Robert, 1996. "A Bayesian approach to additive semiparametric regression," Journal of Econometrics, Elsevier, vol. 74(2), pages 209-235, October.

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