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Original Articles

Computing exact score vectors for linear Gaussian state space models

Pages 2313-2326 | Received 21 Aug 2018, Accepted 25 Mar 2019, Published online: 22 Apr 2019

References

  • Astrom, K. J. 1981. Maximum likelihood and prediction error methods. In Trends and progress in system identification, ed. P. Eykhoff, 145–168. Oxford, UK: Pergamon Press.
  • Davidson, R., and J. G. MacKinnon. 1993. Estimation and inference in econometrics. New York: Oxford University Press.
  • Harvey, A. C. 1989. Forecasting, structural time series models and the Kalman filter. Cambridge: Academic Press.
  • Hooker, M. A. 1994. Analytic first and second derivatives for the recursive prediction error algorithm’s log likelihood function. IEEE Transactions on Automatic Control 39 (3):662–4. doi:10.1109/9.280783.
  • Koopman, S. J., and N. Shephard. 1992. Exact score for time series models in state space form. Biometrika 79:823–6. doi:10.2307/2337237.
  • Magnus, J. R., and H. Neudecker. 1979. The commutation matrix: some properties and applications. The Annals of Statistics 7 (2):381–94. doi:10.1214/aos/1176344621.
  • Magnus, J. R., and H. Neudecker. 1999. Matrix differential calculus with applications in statistics and econometrics. revised edition, New York: John Wiley & Sons.
  • Nagakura, D. 2013. Explicit vector expression of exact score for time series models in state space form. Statistical Methodology 13 :69–74. doi:10.1016/j.stamet.2013.01.003.
  • Nagakura, D. 2019. Testing for random coefficient autoregressive and stochastic unit root models. Working Paper. SSRN: https://ssrn.com/abstract=3358301
  • Nagakura, D., and Y. Takano. 2019. Tests for volatility dynamics in bivariate stochastic volatility models. Working Paper. SSRN: https://ssrn.com/abstract=3330410 or http://dx.doi.org/10.2139/ssrn.3330410
  • Neudecker, H., and T. Wansbeek. 1983. Some results on commutation matrices, with statistical applications. Canadian Journal of Statistics 11 (3):221–31. doi:10.2307/3314625.
  • Sandell, N. R., Jr., and K. I. Yared. 1978. Maximum likelihood identification of state space models for linear dynamic systems, electronic systems laboratory. MIT, Cambridge. MA. Rep. ESL-R-814, April.
  • Segal, M., and E. Weinstein. 1989. A new method for evaluating the log-likelihood gradient, the Hessian, and the Fisher Information matrix for linear dynamic systems. IEEE Transactions on Information Theory 35 (3):682–7. doi:10.1109/18.30995.

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