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The estimation of a state space model by estimating functions with an application

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  • Demetrios Papanastassiou
  • Demetrios Ioannides

Abstract

Conventionally the parameters of a linear state space model are estimated by maximizing a Gaussian likelihood function, even when the input errors are not Gaussian. In this paper we propose estimation by estimating functions fulfilling Godambe's optimality criterion. We discuss the issue of an unknown starting state vector, and we also develop recursive relations for the third‐ and fourth‐order moments of the state predictors required for the calculations. We conclude with a simulation study demonstrating the proposed procedure on the estimation of the stochastic volatility model. The results suggest that the new estimators outperform the Gaussian likelihood.

Suggested Citation

  • Demetrios Papanastassiou & Demetrios Ioannides, 2004. "The estimation of a state space model by estimating functions with an application," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(4), pages 407-427, November.
    • Handle: RePEc:bla:stanee:v:58:y:2004:i:4:p:407-427
    DOI: 10.1111/j.1467-9574.2004.00268.x
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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.
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