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Keywords:

  • Stochastic differential equations;
  • continuous/discrete state space model:discrete measurements;
  • maximum likelihood estimation;
  • analytical derivatives;
  • scoring;
  • EM

Abstract. Maximum likelihood estimation of sampled continuous-time stochastic processes is considered. The likelihood is directly maximized with respect to the original structural parameters using a scoring algorithm with exact analytical derivatives. Furthermore, the case of unobserved states and errors of measurement is treated via EM and quasi-Newton algorithms. The proposed methods are illustrated with simulation studies and analysis of sunspot activity.