Monte Carlo maximum likelihood estimation for non-Gaussian state space models

J. Durbin*, S. J. Koopman

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

State space models are considered for observations which have non-Gaussian distributions. We obtain accurate approximations to the loglikelihood for such models by Monte Carlo simulation. Devices are introduced which improve the accuracy of the approximations and which increase computational efficiency. The loglikelihood function is maximised numerically to obtain estimates of the unknown hyperparameters. Standard errors of the estimates due to simulation are calculated. Details are given for the important special cases where the observations come from an exponential family distribution and where the observation equation is linear but the observation errors are non-Gaussian. The techniques are illustrated with a series for which the observations have a Poisson distribution and a series for which the observation errors have a t-distribution.

Original languageEnglish
Pages (from-to)669-684
Number of pages16
JournalBiometrika
Volume84
Issue number3
DOIs
Publication statusPublished - 1 Jan 1997
Externally publishedYes

Keywords

  • Antithetic variable
  • Control variable
  • Exponential family distribution
  • Heavy-tailed distribution
  • Importance sampling
  • Kalman filtering and smoothing
  • Monte Carlo simulation
  • Non-Gaussian time series model

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